Method and device for predicting physiological values

ABSTRACT

The invention relates generally to methods, systems, and devices for measuring the concentration of target analytes present in a biological system using a series of measurements obtained from a monitoring system and a Mixtures of Experts (MOE) algorithm. In one embodiment, the present invention describes a method for measuring blood glucose in a subject.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 09/241,929, filed 1 Feb. 1999, which is a continuation-in-partof U.S. patent application Ser. No. 09/198,039, filed 23 Nov. 1998,which is a continuation-in-part of U.S. patent application Ser. No.09/163,856, filed 30 Sep. 1998, all applications are herein incorporatedby reference in their entireties.

FIELD OF THE INVENTION

The invention relates generally to a method and device for measuring theconcentration of target chemical analytes present in a biologicalsystem. More particularly, the invention relates to a method andmonitoring systems for predicting a concentration of an analyte using aseries of measurements obtained from a monitoring system and a Mixturesof Experts (MOE) algorithm.

BACKGROUND OF THE INVENTION

The Mixtures of Experts model is a statistical method for classificationand regression (Waterhouse, S., “Classification and Regression UsingMixtures of Experts, October 199.7, Ph.D. Thesis, Cambridge University).Waterhouse discusses Mixtures of Experts models from a theoreticalperspective and compares them with other models, such as, trees,switching regression models, modular networks. The first extensiondescribed in Waterhouse's thesis is a constructive algorithm forlearning model architecture and parameters, which is inspired byrecursive partitioning. The second extension described in Waterhouse'sthesis uses Bayesian methods for learning the parameters of the model.These extensions are compared empirically with the standard Mixtures ofExperts model and with other statistical models on small to medium sizeddata sets. Waterhouse also describes the application of the Mixtures ofExperts framework to acoustic modeling within a large vocabulary speechrecognition system.

The Mixtures of Experts model has been employed in protein secondarystructure prediction (Barlow, T. W., Journal Of Molecular Graphics, 13(3), p. 175-183, 1995). In this method input data were clustered andused to train a series different networks. Application of a HierarchicalMixtures of Experts to the prediction of protein secondary structure wasshown to provide no advantages over a single network.

Mixtures of Experts algorithms have also been applied to the analysis ofa variety of different kinds of data sets including the following: humanmotor systems (Ghahramani, Z. and Wolpert, D. M., Nature,386(6623):392-395, 1997); and economic analysis (Hamilton, J. D. andSusmel, R., Journal of Econometrics, 64(1-2):307-333, 1994).

SUMMARY OF THE INVENTION

The present invention provides a method and device (for example, amonitoring or sampling system) for continually or continuously measuringthe concentration of an analyte present in a biological system. Themethod entails continually or continuously detecting a raw signal fromthe biological system, wherein the raw signal is specifically related tothe analyte. A calibration step is performed to correlate the raw signalwith a measurement value indicative of the concentration of analytepresent in the biological system. These steps of detection andcalibration are used to obtain a series of measurement values atselected time intervals. Once the series of measurement values isobtained, the method of the invention provides for the prediction of ameasurement value using a Mixtures of Experts (MOE) algorithm.

The raw signal can be obtained using any suitable sensing methodologyincluding, for example, methods which rely on direct contact of asensing apparatus with the biological system; methods which extractsamples from the biological system by invasive, minimally invasive, andnon-invasive sampling techniques, wherein the sensing apparatus iscontacted with the extracted sample; methods which rely on indirectcontact of a sensing apparatus with the biological system; and the like.In preferred embodiments of the invention, methods are used to extractsamples from the biological sample using minimally invasive ornon-invasive sampling techniques. The sensing apparatus used with any ofthe above-noted methods can employ any suitable sensing element toprovide the raw signal including, but not limited to, physical,chemical, electrochemical, photochemical, spectrophotometric,polarimetric, calorimetric, radiometric, or like elements. In preferredembodiments of the invention, a biosensor is used which comprises anelectrochemical sensing element.

In one particular embodiment of the invention, the raw signal isobtained using a transdermal sampling system that is placed in operativecontact with a skin or mucosal surface of the biological system. Thesampling system transdermally extracts the analyte from the biologicalsystem using any appropriate sampling technique, for example,iontophoresis. The transdermal sampling system is maintained inoperative contact with the skin or mucosal surface of the biologicalsystem to provide for continual or continuous analyte measurement.

In a preferred embodiment of the invention, a Mixtures of Expertsalgorithm is used to predict measurement values. The general Mixtures ofExperts algorithm is represented by the following series of equations:where the individual experts have a linear form:

$\begin{matrix}{{An} = {\sum\limits_{i = 1}^{n}{{An}_{i}w_{i}}}} & (1)\end{matrix}$

wherein (An) is an analyte of interest, n is the number of experts,An_(i) is the analyte predicted by Expert i; and w_(i) is a parameter,and the individual experts An_(i) are further defined by the expressionshown as Equation (2)

$\begin{matrix}{{An}_{i} = {{\sum\limits_{j = 1}^{m}{a_{ij}P_{j}}} + z_{i}}} & (2)\end{matrix}$

wherein, An_(i) is the analyte predicted by Expert i; P_(j) is one of mparameters, m is typically less than 100; a_(ij) are coefficients; andz_(i) is a constant; and further where the weighting value, w_(i), isdefined by the formula shown as Equation (3).

$\begin{matrix}{w_{i} = \frac{^{d_{i}}}{\left\lbrack {\sum\limits_{k = 1}^{n}^{d_{k}}} \right\rbrack}} & (3)\end{matrix}$

where e refers to the exponential function and the d_(k) (note that thed_(i) in the numerator of Equation 3 is one of the d_(k)) are aparameter set analogous to Equation 2 that is used to determine theweights w_(i). The d_(k) are given by Equation 4.

$\begin{matrix}{d_{k} = {{\sum\limits_{j = 1}^{m}{\alpha_{jk}P_{j}}} + \omega_{k}}} & (4)\end{matrix}$

where α_(jk) is a coefficient, P_(j) is one of m parameters, and whereω_(k) is a constant.

Another object of the invention to use the Mixtures of Experts algorithmof the invention to predict blood glucose values. In one aspect, themethod of the invention is used in conjunction with an iontophoreticsampling device that provides continual or continuous blood glucosemeasurements. In one embodiment the Mixtures of Experts algorithm isessentially as follows: where the individual experts have a linear form

BG=w ₁ BG ₁ +w ₂ BG ₂ +w ₃ BG ₃  (5)

wherein (BG) is blood glucose, there are three experts (n=3) and BG_(i)is the analyte predicted by Expert i; w_(i) is a parameter, and theindividual Experts BG_(i) are further defined by the expression shown asEquations 6, 7, and 8

BG ₁ =p ₁(time)+q ₁(active)+r ₁(signal)+s ₁(BG|cp)+t ₁  (6)

BG ₂ =p ₂(time)+q ₂(active)+r ₂(signal)+s ₂(BG|cp)+t ₂  (7)

BG ₃ =p ₃(time)+q ₃(active)+r ₃(signal)+s ₃(BG|cp)+t ₃  (8)

wherein, BG_(i) is the analyte predicted by Expert i; parametersinclude, time (elapsed time since the sampling system was placed inoperative contact with said biological system), active (active signal),signal (calibrated signal), and BG/cp (blood glucose value at acalibration point); p_(i), q_(i), r_(i), and s_(i) are coefficients; andt_(i) is a constant; and further where the weighting value, w_(i), isdefined by the formulas shown as Equations 9, 10, and 11

$\begin{matrix}{w_{1} = \frac{^{d_{1}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (9) \\{w_{2} = \frac{^{d_{2}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (10) \\{w_{3} = \frac{^{d_{3}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (11)\end{matrix}$

where e refers to the exponential function and d_(i) is a parameter set(analogous to Equations 6, 7, and 8) that are used to determine theweights w_(i), given by Equations 9, 10, and 11, and

d ₁=τ₁(time)+β₁(active)+γ₁(signal)+δ₁(BG|cp)+∈₁  (12)

d ₂=τ₂(time)+β₂(active)+γ₂(signal)+δ₂(BG|cp)+∈₂  (13)

d ₃=τ₃(time)+β₃(active)+γ₃(signal)+δ₃(BG|cp)+∈₃  (14)

where τ_(i), β_(i), γ_(i) and δ_(i) are coefficients, and where ∈_(i) isa constant.

In another embodiment for the prediction of blood glucose values, theMixtures of Experts algorithm is essentially as follows: where theindividual experts have a linear form

BG=w ₁ BG ₁ +w ₂ BG ₂ +w ₃ BG ₃  (15)

wherein (BG) is blood glucose, there are three experts (n=3) and BG_(i)is the analyte predicted by Expert i; w_(i) is a parameter, and theindividual Experts BG_(i) are further defined by the expression shown asEquations 16, 17, and 18

BG ₁ =p ₁(time_(c))+q ₁(active)+r ₁(signal)+s ₁(BG|cp)+t ₁  (16)

BG ₂ =p ₂(time_(c))+q ₂(active)+r ₂(signal)+s ₂(BG|cp)+t ₂  (17)

BG ₃ =p ₃(time_(c))+q ₃(active)+r ₃(signal)+s ₃(BG|cp)+t ₃  (18)

wherein, BG_(i) is the analyte predicted by Expert i; parametersinclude, time_(c) (elapsed time since calibration of said samplingsystem), active (active signal), signal (calibrated signal), and BG/cp(blood glucose value at a calibration point); p_(i), q_(i), r_(i), ands_(i) are coefficients; and t_(i) is a constant; and further where theweighting value, w_(i), is defined by the formulas shown as Equations19, 20, and 21

$\begin{matrix}{w_{1} = \frac{^{d_{1}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (19) \\{w_{2} = \frac{^{d_{2}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (20) \\{w_{3} = \frac{^{d_{3}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (21)\end{matrix}$

where e refers to the exponential function and d_(i) is a parameter set(analogous to Equations 6, 7, and 8) that are used to determine theweights w_(i), given by Equations 19, 20, and 21, and

d ₁=τ₁(time_(c))+β₁(active)+γ₁(signal)+δ₁(BG|cp)+∈₁  (22)

d ₂=τ₂(time_(c))+β₂(active)+γ₂(signal)+δ₂(BG|cp)+∈₂  (23)

d ₃=τ₃(time_(c))+β₃(active)+γ₃(signal)+δ₃(BG|cp)+∈₃  (24)

where τ_(i), β_(i), γ_(i) and δ_(i) are coefficients, and where ∈_(i) isa constant.

Parameters can be substituted, and/or other parameters can be includedin these calculations, for example, time parameters can be varied (e.g.,as described above, elapsed time since the sampling system was placed incontact with a biological system, or elapsed time since the samplingsystem was calibrated) or multiple time parameters can be used in thesame equation where these parameters are appropriately weighted. Furtherparameters include, but are not limited to, temperature, ionophoreticvoltage, and skin conductivity. In addition, a calibration check can beused to insure an efficacious calibration.

A further object of the invention to provide a method for measuring ananalyte, for example, blood glucose, in a subject. In one embodiment,the method entails operatively contacting a glucose sensing apparatuswith the subject to detect blood glucose and thus obtain a raw signalfrom the sensing apparatus. The raw signal is specifically related tothe glucose, and is converted into a measurement value indicative of thesubject's blood glucose concentration using a calibration step. In oneaspect of the invention, the sensing apparatus is a near-IRspectrometer. In another aspect of the invention, the sensing meanscomprises a biosensor having an electrochemical sensing element.

It is also an object of the invention to provide a monitoring system forcontinually or continuously measuring an analyte present in a biologicalsystem. The monitoring system is formed from the operative combinationof a sampling means, a sensing means, and a microprocessor means whichcontrols the sampling means and the sensing means. The sampling means isused to continually or continuously extract the analyte from thebiological system across a skin or mucosal surface of said biologicalsystem. The sensing means is arranged in operative contact with theanalyte extracted by the sampling means, such that the sensing means canobtain a raw signal from the extracted analyte which signal isspecifically related to the analyte. The microprocessor meanscommunicates with the sampling means and the sensing means, and is usedto: (a) control the sampling means and the sensing means to obtain aseries of raw signals at selected time intervals during a continual orcontinuous measurement period; (b) correlate the raw signals withmeasurement values indicative of the concentration of analyte present inthe biological system; and (c) predict a measurement value using theMixtures of Experts algorithm. In one aspect, the monitoring system usesan iontophoretic current to extract the analyte from the biologicalsystem.

It is a further object of the invention to provide a monitoring systemfor measuring blood glucose in a subject. The monitoring system isformed from an operative combination of a sensing means and amicroprocessor means. The sensing means is adapted for operative contactwith the subject or with a glucose-containing sample extracted from thesubject, and is used to obtain a raw signal specifically related toblood glucose in the subject. The microprocessor means communicates withthe sensing means, and is used to: (a) control the sensing means toobtain a series of raw signals (specifically related to blood glucose)at selected time intervals; (b) correlate the raw signals withmeasurement values indicative of the concentration of blood glucosepresent in the subject; and (c) predict a measurement value using theMixtures of Experts algorithm.

In a further aspect, the monitoring system comprises a biosensor havingan electrochemical sensing element. In another aspect, the monitoringsystem comprises a near-IR spectrometer.

Additional objects, advantages and novel features of the invention willbe set forth in part in the description which follows, and in part willbecome apparent to those skilled in the art upon examination of thefollowing, or may be learned by practice of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A depicts a top plan view of an iontophoretic collection reservoirand electrode assembly for use in a transdermal sampling deviceconstructed according to the present invention.

FIG. 1B depicts the side view of the iontophoretic collection reservoirand electrode assembly shown in FIG. 1A.

FIG. 2 is a pictorial representation of an iontophoretic sampling devicewhich includes the iontophoretic collection reservoir and electrodeassembly of FIGS. 1A and 1B.

FIG. 3 is an exploded pictorial representation of components from apreferred embodiment of the automatic sampling system of the presentinvention.

FIG. 4 is a representation of one embodiment of a bimodal electrodedesign. The figure presents an overhead and schematic view of theelectrode assembly 433. In the figure, the bimodal electrode is shown at430 and can be, for example, a Ag/AgCl iontophoretic/counter electrode.The sensing or working electrode (made from, for example, platinum) isshown at 431. The reference electrode is shown at 432 and can be, forexample, a Ag/AgCl electrode. The components are mounted on a suitablenonconductive substrate 434, for example, plastic or ceramic. Theconductive leads 437 (represented by dotted lines) leading to theconnection pad 435 are covered by a second nonconductive piece 436 (thearea represented by vertical striping) of similar or different material(e.g., plastic or ceramic). In this example of such an electrode theworking electrode area is approximately 1.35 cm². The dashed line inFIG. 4 represents the plane of the cross-sectional schematic viewpresented in FIG. 5.

FIG. 5 is a representation of a cross-sectional schematic view of thebimodal electrodes as they may be used in conjunction with a referenceelectrode and a hydrogel pad. In the figure, the components are asfollows: bimodal electrodes 540 and 541; sensing electrodes 542 and 543;reference electrodes 544 and 545; a substrate 546; and hydrogel pads 547and 548.

FIG. 6 depicts predicted blood glucose data (using the Mixtures ofExperts algorithm) versus measured blood glucose data, as described inExample 2.

FIG. 7 depicts predicted blood glucose data (using the Mixtures ofExperts algorithm) versus measured blood glucose data, as described inExample 4.

FIG. 8 presents a graph of the measured and predicted blood glucoselevels vs. time, as described in Example 4.

FIG. 9 depicts an exploded view of an embodiment of an autosensor.

FIGS. 10A and 10B graphically illustrate the method of the presentinvention used for decreasing the bias of a data set.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Before describing the present invention in detail, it is to beunderstood that this invention is not limited to particular compositionsor biological systems, as such may vary. It is also to be understoodthat the terminology used herein is for the purpose of describingparticular embodiments only, and is not intended to be limiting.

It must be noted that, as used in this specification and the appendedclaims, the singular forms “a”, “an” and “the” include plural referentsunless the content clearly dictates otherwise. Thus, for example,reference to “an analyte” includes mixtures of analytes, and the like.

All publications, patents and patent applications cited herein, whethersupra or infra, are hereby incorporated by reference in their entirety.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which the invention pertains. Although any methods andmaterials similar or equivalent to those described herein can be used inthe practice for testing of the present invention, the preferredmaterials and methods are described herein.

In describing and claiming the present invention, the followingterminology will be used in accordance with the definitions set outbelow.

1.0.0 DEFINITIONS

The terms “analyte” and “target analyte” are used herein to denote anyphysiological analyte of interest that is a specific substance orcomponent that is being detected and/or measured in a chemical,physical, enzymatic, or optical analysis. A detectable signal (e.g., achemical signal or electrochemical signal) can be obtained, eitherdirectly or indirectly, from such an analyte or derivatives thereof.Furthermore, the terms “analyte” and “substance” are usedinterchangeably herein, and are intended to have the same meaning, andthus encompass any substance of interest. In preferred embodiments, theanalyte is a physiological analyte of interest, for example, glucose, ora chemical that has a physiological action, for example, a drug orpharmacological agent.

A “sampling device” or “sampling system” refers to any device forobtaining a sample from a biological system for the purpose ofdetermining the concentration of an analyte of interest. As used herein,the term “sampling” means invasive, minimally invasive or non-invasiveextraction of a substance from the biological system, generally across amembrane such as skin or mucosa. The membrane can be natural orartificial, and can be of plant or animal nature, such as natural orartificial skin, blood vessel tissue, intestinal tissue, and the like.Typically, the sampling means are in operative contact with a“reservoir,” or “collection reservoir,” wherein the sampling means isused for extracting the analyte from the biological system into thereservoir to obtain the analyte in the reservoir. A “biological system”includes both living and artificially maintained systems. Examples ofminimally invasive and noninvasive sampling techniques includeiontophoresis, sonophoresis, suction, electroporation, thermal poration,passive diffusion, microfine (miniature) lances or cannulas,subcutaneous implants or insertions, and laser devices. Sonophoresisuses ultrasound to increase the permeability of the skin (see, e.g.,Menon et al. (1994) Skin Pharmacology 7:130-139). Suitable sonophoresissampling systems are described in International Publication No. WO91/12772, published 5 Sep. 1991. Passive diffusion sampling devices aredescribed, for example, in International Publication Nos.: WO 97/38126(published 16 Oct. 1997); WO 97/42888, WO 97/42886, WO 97/42885, and WO97/42882 (all published 20 Nov. 1997); and WO 97/43962 (published 27Nov. 1997). Laser devices use a small laser beam to burn a hole throughthe upper layer of the patient's skin (see, e.g., Jacques et al. (1978)J. Invest. Dermatology 88:88-93). Examples of invasive samplingtechniques include traditional needle and syringe or vacuum sample tubedevices.

The term “collection reservoir” is used to describe any suitablecontainment means for containing a sample extracted from a biologicalsystem. For example, the collection reservoir can be a receptaclecontaining a material which is ionically conductive (e.g., water withions therein), or alternatively, it can be a material, such as, asponge-like material or hydrophilic polymer, used to keep the water inplace. Such collection reservoirs can be in the form of a hydrogel (forexample, in the form of a disk or pad). Hydrogels are typically referredto as “collection inserts.” Other suitable collection reservoirsinclude, but are not limited to, tubes, vials, capillary collectiondevices, cannulas, and miniaturized etched, ablated or molded flowpaths.

A “housing” for the sampling system can further include suitableelectronics (e.g., microprocessor, memory, display and other circuitcomponents) and power sources for operating the sampling system in anautomatic fashion.

A “monitoring system,” as used herein, refers to a system useful forcontinually or continuously measuring a physiological analyte present ina biological system. Such a system typically includes, but is notlimited to, sampling means, sensing means, and a microprocessor means inoperative communication with the sampling means and the sensing means.

The term “artificial,” as used herein, refers to an aggregation of cellsof monolayer thickness or greater which are grown or cultured in vivo orin vitro, and which function as a tissue of an organism but are notactually derived, or excised, from a pre-existing source or host.

The term “subject” encompasses any warm-blooded animal, particularlyincluding a member of the class Mammalia such as, without limitation,humans and nonhuman primates such as chimpanzees and other apes andmonkey species; farm animals such as cattle, sheep, pigs, goats andhorses; domestic mammals such as dogs and cats; laboratory animalsincluding rodents such as mice, rats and guinea pigs, and the like. Theterm does not denote a particular age or sex. Thus, adult and newbornsubjects, as well as fetuses, whether male or female, are intended to becovered.

As used herein, the term “continual measurement” intends a series of twoor more measurements obtained from a particular biological system, whichmeasurements are obtained using a single device maintained in operativecontact with the biological system over the time period in which theseries of measurements is obtained. The term thus includes continuousmeasurements.

The term “transdermal,” as used herein, includes both transdermal andtransmucosal techniques, i.e., extraction of a target analyte acrossskin or mucosal tissue. Aspects of the invention which are describedherein in the context of “transdermal,” unless otherwise specified, aremeant to apply to both transdermal and transmucosal techniques.

The term “transdermal extraction,” or “transdermally extracted” intendsany noninvasive, or at least minimally invasive sampling method, whichentails extracting and/or transporting an analyte from beneath a tissuesurface across skin or mucosal tissue. The term thus includes extractionof an analyte using iontophoresis (reverse iontophoresis),electroosmosis, sonophoresis, microdialysis, suction, and passivediffusion. These methods can, of course, be coupled with application ofskin penetration enhancers or skin permeability enhancing technique suchas tape stripping or pricking with micro-needles. The term“transdermally extracted” also encompasses extraction techniques whichemploy thermal poration, electroporation, microfine lances, microfinecanulas, subcutaneous implants or insertions, and the like.

The term “iontophoresis” intends a method for transporting substancesacross tissue by way of an application of electrical energy to thetissue. In conventional iontophoresis, a reservoir is provided at thetissue surface to serve as a container of material to be transported.Iontophoresis can be carried out using standard methods known to thoseof skill in the art, for example, by establishing an electricalpotential using a direct current (DC) between fixed anode and cathode“iontophoretic electrodes,” alternating a direct current between anodeand cathode iontophoretic electrodes, or using a more complex waveformsuch as applying a current with alternating polarity (AP) betweeniontophoretic electrodes (so that each electrode is alternately an anodeor a cathode).

The term “reverse iontophoresis” refers to the movement of a substancefrom a biological fluid across a membrane by way of an applied electricpotential or current. In reverse iontophoresis, a reservoir is providedat the tissue surface to receive the extracted material.

“Electroosmosis” refers to the movement of a substance through amembrane by way of an electric field-induced convective flow. The termsiontophoresis, reverse iontophoresis, and electroosmosis, will be usedinterchangeably herein to refer to movement of any ionically charged oruncharged substance across a membrane (e.g., an epithelial membrane)upon application of an electric potential to the membrane through anionically conductive medium.

The term “sensing device,” “sensing means,” or “biosensor device”encompasses any device that can be used to measure the concentration ofan analyte, or derivative thereof, of interest. Preferred sensingdevices for detecting blood analytes generally include electrochemicaldevices and chemical devices. Examples of electrochemical devicesinclude the Clark electrode system (see, e.g., Updike, et al., (1967)Nature 214:986-988), and other amperometric, coulometric, orpotentiometric electrochemical devices. Examples of chemical devicesinclude conventional enzyme-based reactions as used in the Lifescan®glucose monitor (Johnson and Johnson, New Brunswick, N.J.) (see, e.g.,U.S. Pat. No. 4,935,346 to Phillips, et al.).

A “biosensor” or “biosensor device” includes, but is not limited to, a“sensor element” which includes, but is not limited to, a “biosensorelectrode” or “sensing electrode” or “working electrode” which refers tothe electrode that is monitored to determine the amount of electricalsignal at a point in time or over a given time period, which signal isthen correlated with the concentration of a chemical compound. Thesensing electrode comprises a reactive surface which converts theanalyte, or a derivative thereof, to electrical signal. The reactivesurface can be comprised of any electrically conductive material suchas, but not limited to, platinum-group metals (including, platinum,palladium, rhodium, ruthenium, osmium, and iridium), nickel, copper,silver, and carbon, as well as, oxides, dioxides, combinations or alloysthereof. Some catalytic materials, membranes, and fabricationtechnologies suitable for the construction of amperometric biosensorswere described by Newman, J. D., et al. (Analytical Chemistry 67(24),4594-4599, 1995).

The “sensor element” can include components in addition to a biosensorelectrode, for example, it can include a “reference electrode,” and a“counter electrode.” The term “reference electrode” is used herein tomean an electrode that provides a reference potential, e.g., a potentialcan be established between a reference electrode and a workingelectrode. The term “counter electrode” is used herein to mean anelectrode in an electrochemical circuit which acts as a current sourceor sink to complete the electrochemical circuit. Although it is notessential that a counter electrode be employed where a referenceelectrode is included in the circuit and the electrode is capable ofperforming the function of a counter electrode, it is preferred to haveseparate counter and reference electrodes because the referencepotential provided by the reference electrode is most stable when it isat equilibrium. If the reference electrode is required to act further asa counter electrode, the current flowing through the reference electrodemay disturb this equilibrium. Consequently, separate electrodesfunctioning as counter and reference electrodes are most preferred.

In one embodiment, the “counter electrode” of the “sensor element”comprises a “bimodal electrode.” The term “bimodal electrode” as usedherein typically refers to an electrode which is capable of functioningnon-simultaneously as, for example, both the counter electrode (of the“sensor element”) and the iontophoretic electrode (of the “samplingmeans”).

The terms “reactive surface,” and “reactive face” are usedinterchangeably herein to mean the surface of the sensing electrodethat: (1) is in contact with the surface of an electrolyte containingmaterial (e.g. gel) which contains an analyte or through which ananalyte, or a derivative thereof, flows from a source thereof; (2) iscomprised of a catalytic material (e.g., carbon, platinum, palladium,rhodium, ruthenium, or nickel and/or oxides, dioxides and combinationsor alloys thereof) or a material that provides sites for electrochemicalreaction; (3) converts a chemical signal (e.g. hydrogen peroxide) intoan electrical signal (e.g., an electrical current); and (4) defines theelectrode surface area that, when composed of a reactive material, issufficient to drive the electrochemical reaction at a rate sufficient togenerate a detectable, reproducibly measurable, electrical signal thatis correlatable with the amount of analyte present in the electrolyte.

An “ionically conductive material” refers to any material that providesionic conductivity, and through which electrochemically active speciescan diffuse. The ionically conductive material can be, for example, asolid, liquid, or semi-solid (e.g., in the form of a gel) material thatcontains an electrolyte, which can be composed primarily of water andions (e.g., sodium chloride), and generally comprises 50% or more waterby weight. The material can be in the form of a gel, a sponge or pad(e.g., soaked with an electrolytic solution), or any other material thatcan contain an electrolyte and allow passage therethrough ofelectrochemically active species, especially the analyte of interest.

The term “physiological effect” encompasses effects produced in thesubject that achieve the intended purpose of a therapy. In preferredembodiments, a physiological effect means that the symptoms of thesubject being treated are prevented or alleviated. For example, aphysiological effect would be one that results in the prolongation ofsurvival in a patient.

A “laminate”, as used herein, refers to structures comprised of at leasttwo bonded layers. The layers may be bonded by welding or through theuse of adhesives. Examples of welding include, but are not limited to,the following: ultrasonic welding, heat bonding, and inductively coupledlocalized heating followed by localized flow. Examples of commonadhesives include, but are not limited to, pressure sensitive adhesives,thermoset adhesives, cyanocrylate adhesives, epoxies, contact adhesives,and heat sensitive adhesives.

A “collection assembly”, as used herein, refers to structures comprisedof several layers, where the assembly includes at least one collectioninsert, for example a hydrogel. An example of a collection assembly ofthe present invention is a mask layer, collection inserts, and aretaining layer where the layers are held in appropriate, functionalrelationship to each other but are not necessarily a laminate, i.e., thelayers may not be bonded together. The layers may, for example, be heldtogether by interlocking geometry or friction.

An “autosensor assembly”, as used herein, refers to structures generallycomprising a mask layer, collection inserts, a retaining layer, anelectrode assembly, and a support tray. The autosensor assembly may alsoinclude liners. The layers of the assembly are held in appropriate,functional relationship to each other:

The mask and retaining layers are preferably composed of materials thatare substantially impermeable to the analyte (chemical signal) to bedetected (e.g., glucose); however, the material can be permeable toother substances. By “substantially impermeable” is meant that thematerial reduces or eliminates chemical signal transport (e.g., bydiffusion). The material can allow for a low level of chemical signaltransport, with the proviso that chemical signal that passes through thematerial does not cause significant edge effects at the sensingelectrode.

“Substantially planar” as used herein, includes a planar surface thatcontacts a slightly curved surface, for example, a forearm or upper armof a subject. A “substantially planar” surface is, for example, asurface having a shape to which skin can conform, i.e., contactingcontact between the skin and the surface.

A “Mixtures of Experts (MOE)” algorithm is used in the practice of thepresent invention. An example of a Mixtures of Experts algorithm usefulin connection with the present invention is represented by the followingequations, where the individual experts have a linear form:

$\begin{matrix}{{An} = {\sum\limits_{i = 1}^{n}{{An}_{i}w_{i}}}} & (1)\end{matrix}$

wherein (An) is an analyte of interest, n is the number of experts,An_(i) is the analyte predicted by Expert i; and w_(i) is a parameter,and the individual experts An_(i) are further defined by the expressionshown as Equation (2)

$\begin{matrix}{{An}_{i} = {{\sum\limits_{j = 1}^{m}{a_{ij}P_{j}}} + z_{i}}} & (2)\end{matrix}$

wherein, An_(i) is the analyte predicted by Expert i; P_(j) is one of mparameters, m is typically less than 100; a_(ij) are coefficients; andz_(i) is a constant; and further where the weighting value, w_(i), isdefined by the formula shown as Equation (3).

$\begin{matrix}{w_{i} = \frac{^{d_{i}}}{\left\lbrack {\sum\limits_{k = 1}^{n}^{d_{k}}} \right\rbrack}} & (3)\end{matrix}$

where e refers to the exponential function the d_(k) (note that thed_(i) in the numerator of Equation 3 is one of the d_(k)) are aparameter set analogous to Equation 2 that is used to determine theweights w_(i). The d_(k) are given by Equation 4.

$\begin{matrix}{d_{k} = {{\sum\limits_{j = 1}^{m}{\alpha_{jk}P_{j}}} + \omega_{k}}} & (4)\end{matrix}$

where α_(jk) is a coefficient, P_(j) is one of m parameters, and whereω_(k) is a constant.

The Mixtures of Experts algorithm is a generalized predictive technologyfor data analysis. This method uses a superposition of multiple linearregressions, along with a switching algorithm, to predict outcomes. Anynumber of input/output variables are possible. The unknown coefficientsin this method are determined by a maximum posterior probabilitytechnique.

The method is typically implemented as follows. An experimental data setof input/output pairs is assembled that spans the expected ranges of allvariables. These variables are then used to train the Mixtures ofExperts (that is, used to determine the unknown coefficients). Thesecoefficients are determined using, for example, the ExpectationMaximization method (Dempster, A. P., N. M. Laird, and D. B. Rubin, J.Royal Statistical Society (Series B-Methodological) 39:(1), 1977). Oncethese coefficients are known, the Mixtures of Experts is easily appliedto a new data set.

“Parameter” as used herein refers to an arbitrary constant or variableso appearing in a mathematical expression that changing it give variouscases of the phenomenon represented (McGraw-Hill Dictionary ofScientific and Technical Terms, S. P. Parker, ed., Fifth Edition,McGraw-Hill Inc., 1994). In the context of the GlucoWatch® monitor(Cygnus, Inc., Redwood City, Calif.), a parameter is a variable thatinfluences the value of the blood glucose level as calculated by analgorithm. For the Mixtures of Experts algorithm, these parametersinclude, but are not limited to, the following: time (e.g., elapsed timesince the monitor was applied to a subject; and/or elapsed time sincecalibration); the active signal; the calibrated signal; the bloodglucose value at the calibration point; the skin temperature; the skinconductivity; and the iontophoretic voltage. Changes in the values ofany of these parameters can be expected to change the value of thecalculated blood glucose value. Parameters can be substituted, and/orother parameters can be included in these calculations, for example,time parameters can be varied (e.g., is elapsed time since the samplingsystem was placed in contact with a biological system, or elapsed timesince the sampling system was calibrated) or multiple time parameterscan be used in the same equation where these parameters areappropriately weighted.

By the term “printed” as used herein is meant a substantially uniformdeposition of an electrode formulation onto one surface of a substrate(i.e., the base support). It will be appreciated by those skilled in theart that a variety of techniques may be used to effect substantiallyuniform deposition of a material onto a substrate, e.g., Gravure-typeprinting, extrusion coating, screen coating, spraying, painting, or thelike.

“Bias” as used herein refers to the difference between the expectedvalue of an estimator and the true value of a parameter. “Bias” is usedin a statistical context, in particular, in estimating the value of aparameter of a probability distribution. For example, in the case of alinear regression wherein

y=mx+b, for x=a,

the bias at “a” equals (ma+b)−a.

“Decay” as used herein refers to a gradual reduction in the magnitude ofa quantity, for example, a current detected using a sensor electrodewhere the current is correlated to the concentration of a particularanalyte and where the detected current gradually reduces but theconcentration of the analyte does not.

2.0.0 GENERAL METHODS

The present invention relates to the analysis of data obtained by use ofa sensing device for measuring the concentration of a target analytepresent in a biological system. In preferred embodiments, the sensingdevice comprises a biosensor. In other preferred embodiments, a samplingdevice is used to extract small amounts of a target analyte from thebiological system, and then sense and/or quantify the concentration ofthe target analyte. Measurement with the biosensor and/or sampling withthe sampling device can be carried out in a continual manner. Continualmeasurement allows for closer monitoring of target analyte concentrationfluctuations.

In the general method of the invention, a raw signal is obtained from asensing device, which signal is related to a target analyte present inthe biological system. The raw signal can be obtained using any suitablesensing methodology including, for example, methods which rely on directcontact of a sensing apparatus with the biological system; methods whichextract samples from the biological system by invasive, minimallyinvasive, and non-invasive sampling techniques, wherein the sensingapparatus is contacted with the extracted sample; methods which rely onindirect contact of a sensing apparatus with the biological system; andthe like. In preferred embodiments of the invention, methods are used toextract samples from the biological sample using minimally invasive ornon-invasive sampling techniques. The sensing apparatus used with any ofthe above-noted methods can employ any suitable sensing element toprovide the signal including, but not limited to, physical, chemical,electrochemical, photochemical, spectrophotometric, polarimetric,calorimetric, radiometric, or like elements. In preferred embodiments ofthe invention, a biosensor is used which comprises an electrochemicalsensing element.

In another embodiment of the invention, a near-IR glucose sensingapparatus is used to detect blood glucose in a subject, and thusgenerate the raw signal. A number of near-IR glucose sensing devicessuitable for use in the present method are known in the art and arereadily available. For example, a near-IR radiation diffuse-reflectionlaser spectroscopy device is described in U.S. Pat. No. 5,267,152 toYang et al. Similar near-IR spectrometric devices are also described inU.S. Pat. No. 5,086,229 to Rosenthal et al. and U.S. Pat. No. 4,975,581to Robinson et al. These near-IR devices use traditional methods ofreflective or transmissive near infrared (near-IR) analysis to measureabsorbance at one or more glucose-specific wavelengths, and can becontacted with the subject at an appropriate location, such as afinger-tip, skin fold, eyelid, or forearm surface to obtain the rawsignal.

The raw signal obtained using any of the above-described methodologiesis then converted into an analyte-specific value of known units toprovide an interpretation of the signal obtained from the sensingdevice. The interpretation uses a mathematical transformation to modelthe relationship between a measured response in the sensing device and acorresponding analyte-specific value (in the present invention, aMixtures of Experts algorithm). Thus, a calibration step is used hereinto relate, for example, an electrochemical signal (detected by abiosensor), or near-IR absorbance spectra (detected with a near-IRdetector) with the concentration of a target analyte in a biologicalsystem.

The predicted analyte values can optionally be used in a subsequent stepto control an aspect of the biological system. In one embodiment,predicted analyte values are used to determine when, and at what level,a constituent should be added to the biological system in order tocontrol an aspect of the biological system. In a preferred embodiment,the analyte value can be used in a feedback control loop to control aphysiological effect in the biological system.

The above general methods can, of course, be used with a wide variety ofbiological systems, target analytes, and/or sensing techniques. Thedetermination of particularly suitable combinations is within the skillof the ordinarily skilled artisan when directed by the instantdisclosure. Although these methods are broadly applicable to measuringany chemical analyte and/or substance in a biological system, theinvention is expressly exemplified for use in a non-invasive,transdermal sampling system which uses an electrochemical biosensor toquantify or qualify glucose or a glucose metabolite.

2.1.0 Obtaining the Raw Signal.

The raw signal can be obtained using any sensing device that isoperatively contacted with the biological system. Such sensing devicescan employ physical, chemical, electrochemical, spectrophotometric,polarimetric, colorimetric, radiometric, or like measurement techniques.In addition, the sensing device can be in direct or indirect contactwith the biological system, or used with a sampling device whichextracts samples from the biological system using invasive, minimallyinvasive or non-invasive sampling techniques. In preferred embodiments,a minimally invasive or non-invasive sampling device is used to obtainsamples from the biological system, and the sensing device comprises abiosensor with an electrochemical sensing element.

The analyte can be any specific substance or component in a biologicalsystem that one is desirous of detecting and/or measuring in a chemical,physical, enzymatic, or optical analysis. Such analytes include, but arenot limited to, amino acids, enzyme substrates or products indicating adisease state or condition, other markers of disease states orconditions, drugs of abuse, therapeutic and/or pharmacologic agents(e.g., theophylline, anti-HIV drugs, lithium, anti-epileptic drugs,cyclosporin, chemotherapeutics), electrolytes, physiological analytes ofinterest (e.g., urate/uric acid, carbonate, calcium, potassium, sodium,chloride, bicarbonate (CO₂), glucose, urea (blood urea nitrogen)lactate/lactic acid, hydroxybutyrate, cholesterol, triglycerides,creatine, creatinine, insulin, hematocrit, and hemoglobin), blood gases(carbon dioxide, oxygen, pH), lipids, heavy metals (e.g., lead, copper),and the like. In preferred embodiments, the analyte is a physiologicalanalyte of interest, for example glucose, or a chemical that has aphysiological action, for example a drug or pharmacological agent.

In order to facilitate detection of the analyte, an enzyme can bedisposed in the collection reservoir, or, if several collectionreservoirs are used, the enzyme can be disposed in several or all of thereservoirs. The selected enzyme is capable of catalyzing a reaction withthe extracted analyte (e.g., glucose) to the extent that a product ofthis reaction can be sensed, e.g., can be detected electrochemicallyfrom the generation of a current which current is detectable andproportional to the concentration or amount of the analyte which isreacted. A suitable enzyme is glucose oxidase which oxidizes glucose togluconic acid and hydrogen peroxide. The subsequent detection ofhydrogen peroxide on an appropriate biosensor electrode generates twoelectrons per hydrogen peroxide molecule which create a current whichcan be detected and related to the amount of glucose entering thedevice. Glucose oxidase (GOx) is readily available commercially and haswell known catalytic characteristics. However, other enzymes can also beused, so long as they specifically catalyze a reaction with an analyteor substance of interest to generate a detectable product in proportionto the amount of analyte so reacted.

In like manner, a number of other analyte-specific enzyme systems can beused in the invention, which enzyme systems operate on much the samegeneral techniques. For example, a biosensor electrode that detectshydrogen peroxide can be used to detect ethanol using an alcohol oxidaseenzyme system, or similarly uric acid with urate oxidase system, ureawith a urease system, cholesterol with a cholesterol oxidase system, andtheophylline with a xanthine oxidase system.

In addition, the oxidase enzyme (used for hydrogen peroxidase-baseddetection) can be replaced with another redox system, for example, thedehydrogenase-enzyme NAD-NADH, which offers a separate route todetecting additional analytes. Dehydrogenase-based sensors can useworking electrodes made of gold or carbon (via mediated chemistry).Examples of analytes suitable for this type of monitoring include, butare not limited to, cholesterol, ethanol, hydroxybutyrate,phenylalanine, triglycerides, and urea. Further, the enzyme can beeliminated and detection can rely on direct electrochemical orpotentiometric detection of an analyte. Such analytes include, withoutlimitation, heavy metals (e.g., cobalt, iron, lead, nickel, zinc),oxygen, carbonate/carbon dioxide, chloride, fluoride, lithium, pH,potassium, sodium, and urea. Also, the sampling system described hereincan be used for therapeutic drug monitoring, for example, monitoringanti-epileptic drugs (e.g., phenytion), chemotherapy (e.g., adriamycin),hyperactivity (e.g., ritalin), and anti-organ-rejection (e.g.,cyclosporin).

In particularly preferred embodiments, a sampling device is used toobtain continual transdermal or transmucosal samples from a biologicalsystem, and the analyte of interest is glucose. More specifically, anon-invasive glucose monitoring device is used to measure changes inglucose levels in an animal subject over a wide range of glucoseconcentrations. The sampling method is based on transdermal glucoseextraction and the sensing method is based on electrochemical detectiontechnology. The device can be contacted with the biological systemcontinuously, and automatically obtains glucose samples in order tomeasure glucose concentration at preprogrammed intervals.

Sampling is carried out continually by non-invasively extracting glucosethrough the skin of the patient using an iontophoretic current. Moreparticularly, an iontophoretic current is applied to a surface of theskin of a subject. When the current is applied, ions or chargedmolecules pull along other uncharged molecules or particles such asglucose which are drawn into a collection reservoir placed on thesurface of the skin. The collection reservoir may comprise any ionicallyconductive material and is preferably in the form of a hydrogel which iscomprised of a hydrophilic material, water and an electrolyte. Thecollection reservoir may further contain an enzyme which catalyzes areaction between glucose and oxygen. The enzyme is preferably glucoseoxidase (GOx) which catalyzes the reaction between glucose and oxygenand results in the production of hydrogen peroxide. The hydrogenperoxide reacts at a catalytic surface of a biosensor electrode,resulting in the generation of electrons which create a detectablebiosensor current (raw signal). Based on the amount of biosensor currentcreated over a given period of time, a measurement is taken, whichmeasurement is related to the amount of glucose drawn into thecollection reservoir over a given period of time. In a preferredembodiment the reaction is allowed to continue until substantially allof the glucose in the collection reservoir has been subjected to areaction and is therefore no longer detectable, and the total biosensorcurrent generated is related to the concentration of glucose in thesubject.

When the reaction is complete, the process is repeated and a subsequentmeasurement is obtained. More specifically, the iontophoretic current isagain applied, glucose is drawn through the skin surface into thecollection reservoir, and the reaction is catalyzed in order to create abiosensor current. These sampling (extraction) and sensing operationsare integrated such that glucose from interstitial fluid directlybeneath the skin surface is extracted into the hydrogel collection padwhere it contacts the GOx enzyme. The GOx enzyme converts glucose andoxygen in the hydrogel to hydrogen peroxide which diffuses to a Pt-basedsensor and reacts with the sensor to regenerate oxygen and formelectrons. The electrons generate an electrical signal that can bemeasured, analyzed, and correlated to blood glucose.

A generalized method for continual monitoring of a physiological analyteis disclosed in International Publication No. WO 97/24059, published 10Jul. 1997, which publication is incorporated herein by reference. Asnoted in that publication, the analyte is extracted into a reservoircontaining a hydrogel which is preferably comprised of a hydrophilicmaterial of the type described in International Publication No. WO97/02811, published 30 Jan. 1997, which publication is incorporatedherein by reference. Suitable hydrogel materials include polyethyleneoxide, polyacrylic acid, polyvinylalcohol and related hydrophilicpolymeric materials combined with water to form an aqueous gel.

In the above non-invasive glucose monitoring device, a biosensorelectrode is positioned on a surface of the hydrogel opposite thesurface contacting the skin. The sensor electrode acts as a detectorwhich detects current generated by hydrogen peroxide in the redoxreaction, or more specifically detects current which is generated by theelectrons generated by the redox reaction catalyzed by the platinumsurface of the electrode. The details of such electrode assemblies anddevices for iontophoretic extraction of glucose are disclosed inInternational Publication No. WO 96/00110, published 4 Jan. 1996, andInternational Publication No. WO 97/10499, published 2 Mar. 1997, whichpublications are also incorporated herein by reference.

Referring now to FIGS. 1A and 1B, one example of an iontophoreticcollection reservoir and electrode assembly for use in a transdermalsensing device is generally indicated at 2. The assembly comprises twoiontophoretic collection reservoirs, 4 and 6, each having a conductivemedium 8, and 10 (preferably hydrogel pads), respectively disposedtherein. First (12) and second (14) ring-shaped iontophoretic electrodesare respectively contacted with conductive medium 8 and 10. The firstiontophoretic electrode 12 surrounds three biosensor electrodes whichare also contacted with the conductive medium 8, a working electrode 16,a reference electrode 18, and a counter electrode 20. A guard ring 22separates the biosensor electrodes from the iontophoretic electrode 12to minimize noise from the iontophoretic circuit. Conductive contactsprovide communication between the electrodes and an associated powersource and control means as described in detail below. A similarbiosensor electrode arrangement can be contacted with the conductivemedium 10, or the medium can not have a sensor means contactedtherewith.

Referring now to FIG. 2, the iontophoretic collection reservoir andelectrode assembly 2 of FIGS. 1A and 1B is shown in exploded view incombination with a suitable iontophoretic sampling device housing 32.The housing can be a plastic case or other suitable structure whichpreferably is configured to be worn on a subjects arm in a mannersimilar to a wrist watch. As can be seen, conductive media 8 and 10(hydrogel pads) are separable from the assembly 2; however, when theassembly 2 and the housing 32 are assembled to provide an operationaliontophoretic sampling device 30, the media are in contact with theelectrodes to provide a electrical contact therewith.

A power source (e.g., one or more rechargeable or nonrechargeablebatteries) can be disposed within the housing 32 or within the straps 34which hold the device in contact with a skin or mucosal surface of asubject. In use, an electric potential (either direct current or a morecomplex waveform) is applied between the two iontophoretic electrodes 12and 14 such that current flows from the first iontophoretic electrode12, through the first conductive medium 8 into the skin or mucosalsurface, and then back out through the second conductive medium 10 tothe second iontophoretic electrode 14. The current flow is sufficient toextract substances including an analyte of interest through the skininto one or both of collection reservoirs 4 and 6. The electricpotential may be applied using any suitable technique, for example, theapplied current density may be in the range of about 0.01 to 0.5 mA/cm².In a preferred embodiment, the device is used for continual orcontinuous monitoring, and the polarity of iontophoretic electrodes 12and 14 is alternated at a rate of about one switch every 10 seconds toabout one switch every hour so that each electrode is alternately acathode or an anode. The housing 32 can further include an optionaltemperature sensing element (e.g., a thermistor, thermometer, orthermocouple device) which monitors the temperature at the collectionreservoirs to enable temperature correction of sensor signals. Thehousing can also include an optional conductance sensing element (e.g.,an integrated pair of electrodes) which monitors conductance at the skinor mucosal surface to enable data screening correction or invalidationof sensor signals.

After a suitable iontophoretic extraction period, one or both of thesensor electrode sets can be activated in order to detect extractedsubstances including the analyte of interest. Operation of theiontophoretic sampling device 30 can be controlled by a controller 36(e.g., a microprocessor), which interfaces with the iontophoreticelectrodes, the sensor electrodes, the power supply, the optionaltemperature and/or conductance sensing elements, a display and otherelectronics. For example, the controller 36 can include a programmable acontrolled circuit source/sink drive for driving the iontophoreticelectrodes. Power and reference voltage are provided to the sensorelectrodes, and signal amplifiers can be used to process the signal fromthe working electrode or electrodes. In general, the controllerdiscontinues the iontophoretic current drive during sensing periods. Asensor confidence loop can be provided for continually monitoring thesampling system to insure proper operations.

User control can be carried out using push buttons located on thehousing 32, and an optional liquid crystal display (LCD) can providevisual prompts, readouts and visual alarm indications. Themicroprocessor generally uses a series of program sequences to controlthe operations of the sampling device, which program sequences can bestored in the microprocessor's read only memory (ROM). Embedded software(firmware) controls activation of measurement and display operations,calibration of analyte readings, setting and display of high and lowanalyte value alarms, display and setting of time and date functions,alarm time, and display of stored readings. Sensor signals obtained fromthe sensor electrodes can be processed before storage and display by oneor more signal processing functions or algorithms which are stored inthe embedded software. The microprocessor can also include anelectronically erasable, programmable, read only memory (EEPROM) forstoring calibration parameters, user settings and all downloadablesequences. A serial communications port allows the device to communicatewith associated electronics, for example, wherein the device is used ina feedback control application to control a pump for delivery of amedicament.

Further, the sampling system can be pre-programmed to begin execution ofits signal measurements (or other functions) at a designated time. Oneapplication of this feature is to have the sampling system in contactwith a subject and to program the sampling system to begin sequenceexecution during the night so that it is available for calibrationimmediately upon waking. One advantage of this feature is that itremoves any need to wait for the sampling system to warm-up beforecalibrating it.

2.1.1 Exemplary Embodiments of the Sampling System

An exemplary method and apparatus for sampling small amounts of ananalyte via transdermal methods is described below in further detail.The method and apparatus are used to detect and/or quantify theconcentration of a target analyte present in a biological system. Thissampling is carried out in a continual manner, and quantification ispossible even when the target analyte is extracted in sub-millimolarconcentrations. Although the method and apparatus are broadly applicableto sampling any chemical analyte and/or substance, the sampling systemis expressly exemplified for use in transdermal sampling and quantifyingor qualifying glucose or a glucose metabolite.

Accordingly, in one aspect, an automatic sampling system is used tomonitor levels of glucose in a biological system. The method can bepracticed using a sampling system (device) which transdermally extractsglucose from the system, in this case, an animal subject. Transdermalextraction is carried out by applying an electrical current orultrasonic radiation to a tissue surface at a collection site. Theelectrical current or ultrasonic radiation is used to extract smallamounts of glucose from the subject into a collection reservoir. Thecollection reservoir is in contact with a biosensor which provides formeasurement of glucose concentration in the subject.

In the practice, a collection reservoir is contacted with a tissuesurface, for example, on the stratum corneum of a patient's skin. Anelectrical or ultrasonic force is then applied to the tissue surface inorder to extract glucose from the tissue into the collection reservoir.Extraction is carried out continually over a period of about 1-24 hours,or longer. The collection reservoir is analyzed, at least periodically,to measure glucose concentration therein. The measured value correlateswith the subject's blood glucose level.

More particularly, one or more collection reservoirs are placed incontact with a tissue surface on a subject. The collection reservoirsare also contacted with an electrode which generates a current (forreverse iontophoretic extraction) or with a source of ultrasonicradiation such as a transducer (for sonophoretic extraction) sufficientto extract glucose from the tissue into the collection reservoir.

The collection reservoir contains an ionically conductive liquid orliquid-containing medium. The conductive medium is preferably a hydrogelwhich can contain ionic substances in an amount sufficient to producehigh ionic conductivity. The hydrogel is formed from a solid material(solute) which, when combined with water, forms a gel by the formationof a structure which holds water including interconnected cells and/ornetwork structure formed by the solute. The solute may be a naturallyoccurring material such as the solute of natural gelatin which includesa mixture of proteins obtained by the hydrolysis of collagen by boilingskin, ligaments, tendons and the like. However, the solute or gelforming material is more preferably a polymer material (including, butnot limited to, polyethylene oxide, polyvinyl alcohol, polyacrylic acid,polyacrylamidomethylpropanesulfonate and copolymers thereof, andpolyvinyl pyrrolidone) present in an amount in the range of more than0.5% and less than 40% by weight, preferably 8 to 12% by weight when ahumectant is also added, and preferably about 15 to 20% by weight whenno humectant is added. Additional materials may be added to thehydrogel, including, without limitation, electrolyte (e.g., a salt),buffer, tackifier, humectant, biocides, preservatives and enzymestabilizers. Suitable hydrogel formulations are described inInternational Publication Nos. WO 97/02811, published 30 Jan. 1997, andWO 96/00110, published 4 Jan. 1996, each of which publications areincorporated herein by reference in their entireties.

Since the sampling system must be operated at very low (electrochemical)background noise levels, the collection reservoir must contain anionically conductive medium that does not include significantelectrochemically sensitive components and/or contaminants. Thus, thepreferred hydrogel composition described hereinabove is formulated usinga judicious selection of materials and reagents which do not addsignificant amounts of electrochemical contaminants to the finalcomposition.

In order to facilitate detection of the analyte, an enzyme is disposedwithin the one or more collection reservoirs. The enzyme is capable ofcatalyzing a reaction with the extracted analyte (in this case glucose)to the extent that a product of this reaction can be sensed, e.g., canbe detected electrochemically from the generation of a current whichcurrent is detectable and proportional to the amount of the analytewhich is reacted. A suitable enzyme is glucose oxidase which oxidizesglucose to gluconic acid and hydrogen peroxide. The subsequent detectionof hydrogen peroxide on an appropriate biosensor electrode generates twoelectrons per hydrogen peroxide molecule which create a current whichcan be detected and related to the amount of glucose entering the device(see FIG. 1). Glucose oxidase (Gox) is readily available commerciallyand has well known catalytic characteristics. However, other enzymes canalso be used, so long as they specifically catalyze a reaction with ananalyte, or derivative thereof (or substance of interest), to generate adetectable product in proportion to the amount of analyte so reacted.

In like manner, a number of other analyte-specific enzyme systems can beused in the sampling system, which enzyme systems operate on much thesame general techniques. For example, a biosensor electrode that detectshydrogen peroxide can be used to detect ethanol using an alcohol oxidaseenzyme system, or similarly uric acid with urate oxidase system,cholesterol with a cholesterol oxidase system, and theophylline with axanthine oxidase system.

The biosensor electrode must be able to detect the glucose analyteextracted into the one or more collection reservoirs even when presentat nominal concentration levels. In this regard, conventionalelectrochemical detection systems which utilize glucose oxidase (GOx) tospecifically convert glucose to hydrogen peroxide, and then detect withan appropriate electrode, are only capable of detecting the analyte whenpresent in a sample in at least mM concentrations. In contrast, thesampling system allows sampling and detection of small amounts ofanalyte from the subject, wherein the analyte is detected atconcentrations on the order of 2 to 4 orders of magnitude lower (e.g.,μM concentration in the reservoir) than presently detectable withconventional systems.

Accordingly, the biosensor electrode must exhibit substantially reducedbackground current relative to prior such electrodes. In oneparticularly preferred embodiment, an electrode is provided whichcontains platinum (Pt) and graphite dispersed within a polymer matrix.The electrode exhibits the following features, each of which areessential to the effective operation of the biosensor: backgroundcurrent in the electrode due to changes in the Pt oxidation state andelectrochemically sensitive contaminants in the electrode formulation issubstantially reduced; and catalytic activity (e.g., non-electrochemicalhydrogen peroxide decomposition) by the Pt in the electrode is reduced.

The Pt-containing electrode is configured to provide a geometric surfacearea of about 0.1 to 3 cm², preferably about 0.5 to 2 cm², and morepreferably about 1 cm². This particular configuration is scaled inproportion to the collection area of the collection reservoir used inthe sampling system, throughout which the extracted analyte and/or itsreaction products will be present. The electrode is specially formulatedto provide a high signal-to-noise ratio (S/N ratio) for this geometricsurface area not heretofore available with prior Pt-containingelectrodes. For example, a Pt-containing electrode constructed for usein the sampling system and having a geometric area of about 1 cm²preferably has a background current on the order of about 20 nA or less(when measured with buffer solution at 0.6V), and has high sensitivity(e.g., at least about 60 nA/μM of H₂O₂ in buffer at 0.6V). In likemanner, an electrode having a geometric area of about 0.1 cm² preferablyhas a background current of about 2 nA or less and sensitivity of atleast about 6 nA/μM of H₂O₂; and an electrode having a geometric area ofabout 3 cm² preferably has a background current of about 60 nA or lessand sensitivity of at least about 180 nA/μM of H₂O₂, both as measured inbuffer at 0.6V. These features provide for a high S/N ratio, for examplea S/N ratio of about 3 or greater. The electrode composition isformulated using analytical- or electronic-grade reagents and solventswhich ensure that electrochemical and/or other residual contaminants areavoided in the final composition, significantly reducing the backgroundnoise inherent in the resultant electrode. In particular, the reagentsand solvents used in the formulation of the electrode are selected so asto be substantially free of electrochemically active contaminants (e.g.,anti-oxidants), and the solvents in particular are selected for highvolatility in order to reduce washing and cure times.

The Pt powder used to formulate the electrode composition is alsosubstantially free from impurities, and the Pt/graphite powders areevenly distributed within the polymer matrix using, for example,co-milling or sequential milling of the Pt and graphite. Alternatively,prior to incorporation into the polymer matrix, the Pt can be sputteredonto the graphite powder, colloidal Pt can be precipitated onto thegraphite powder (see, e.g., U.K. patent application number GB 2,221,300,published 31 Jan. 1990, and references cited therein), or the Pt can beadsorbed onto the graphite powder to provide an even distribution of Ptin contact with the conductive graphite. In order to improve the S/Nratio of the electrode, the Pt content in the electrode is lowerrelative to prior Pt or Pt-based electrodes. In a preferred embodiment,the overall Pt content is about 3-7% by weight. Although decreasing theoverall amount of Pt may reduce the sensitivity of the electrode, theinventors have found that an even greater reduction in background noiseis also achieved, resulting in a net improvement in signal-to-noisequality.

The Pt/graphite matrix is supported by a suitable binder, such as anelectrochemically inert polymer or resin binder, which is selected forgood adhesion and suitable coating integrity. The binder is alsoselected for high purity, and for absence of components withelectrochemical background. In this manner, no electrochemicallysensitive contaminants are introduced into the electrode composition byway of the binder. A large number of suitable such binders are known inthe art and are commercially available, including, without limitation,vinyl, acrylic, epoxy, phenoxy and polyester polymers, provided that thebinder or binders selected for the formulation are adequately free ofelectroactive impurities.

The Pt/graphite biosensor electrodes formulated above exhibit reducedcatalytic activity (e.g., passive or non-electrochemical hydrogenperoxide degradation) relative to prior Pt-based electrode systems, andthus have substantially improved signal-to-noise quality. In preferredPt/graphite electrode compositions, the biosensor exhibits about 10-25%passive hydrogen peroxide degradation.

Once formulated, the electrode composition is affixed to a suitablenonconductive surface which may be any rigid or flexible material havingappropriate insulating and/or dielectric properties. The electrodecomposition can be affixed to the surface in any suitable pattern orgeometry, and can be applied using various thin film techniques, such assputtering, evaporation, vapor phase deposition, or the like; or usingvarious thick film techniques, such as film laminating, electroplating,or the like. Alternatively, the composition can be applied using screenprinting, pad printing, inkjet methods, transfer roll printing, orsimilar techniques. Preferably, the electrode is applied using a lowtemperature screen print onto a polymeric substrate. The screening canbe carried out using a suitable mesh, ranging from about 100-400 mesh.

As glucose is transdermally extracted into the collection reservoir, theanalyte reacts with the glucose oxidase within the reservoir to producehydrogen peroxide. The presence of hydrogen peroxide generates a currentat the biosensor electrode that is directly proportional to the amountof hydrogen peroxide in the reservoir. This current provides a signalwhich can be detected and interpreted by an associated system controllerto provide a glucose concentration value for display. In particularembodiments, the detected current can be correlated with the subject'sblood glucose concentration so that the system controller may displaythe subject's actual blood glucose concentration as measured by thesampling system. For example, the system can be calibrated to thesubject's actual blood glucose concentration by sampling the subject'sblood during a standard glucose tolerance test, and analyzing the bloodglucose using both a standard blood glucose monitor and the samplingsystem. In this manner, measurements obtained by the sampling system canbe correlated to actual values using known statistical techniques.

In one preferred embodiment, the automatic sampling system transdermallyextracts the sample in a continual manner over the course of a 1-24 hourperiod, or longer, using reverse iontophoresis. More particularly, thecollection reservoir contains an ionically conductive medium, preferablythe hydrogel medium described hereinabove. A first iontophoresiselectrode is contacted with the collection reservoir (which is incontact with a target tissue surface), and a second iontophoresiselectrode is contacted with either a second collection reservoir incontact with the tissue surface, or some other ionically conductivemedium in contact with the tissue. A power source provides an electricpotential between the two electrodes to perform reverse iontophoresis ina manner known in the art. As discussed above, the biosensor selected todetect the presence, and possibly the level, of the target analyte(glucose) within a reservoir is also in contact with the reservoir.

In practice, an electric potential (either direct current or a morecomplex waveform) is applied between the two iontophoresis electrodessuch that current flows from the first electrode through the firstconductive medium into the skin, and back out from the skin through thesecond conductive medium to the second electrode. This current flowextracts substances through the skin into the one or more collectionreservoirs through the process of reverse iontophoresis orelectroosmosis. The electric potential may be applied as described inInternational Publication No. WO 96/00110, published 4 Jan. 1996.

As an example, to extract glucose, the applied electrical currentdensity on the skin or tissue is preferably in the range of about 0.01to about 2 mA/cm². In a preferred embodiment, in order to facilitate theextraction of glucose, electrical energy is applied to the electrodes,and the polarity of the electrodes is alternated at a rate of about oneswitch every 7.5 minutes (for a 15 minute extraction period), so thateach electrode is alternately a cathode or an anode. The polarityswitching can be manual or automatic.

Any suitable iontophoretic electrode system can be employed, however itis preferred that a silver/silver chloride (Ag/AgCl) electrode system isused. The iontophoretic electrodes are formulated using two criticalperformance parameters: (1) the electrodes are capable of continualoperation for extended periods, preferably periods of up to 24 hours orlonger; and (2) the electrodes are formulated to have highelectrochemical purity in order to operate within the present systemwhich requires extremely low background noise levels. The electrodesmust also be capable of passing a large amount of charge over the lifeof the electrodes.

In an alternative embodiment, the sampling device can operate in analternating polarity mode necessitating the presence of a first andsecond bimodal electrodes (FIGS. 5, 540 and 541) and two collectionreservoirs (FIGS. 5, 547 and 548). Each bi-modal electrode (FIG. 4, 430;FIGS. 5, 540 and 541) serves two functions depending on the phase of theoperation: (1) an electro-osmotic electrode (or iontophoretic electrode)used to electrically draw analyte from a source into a collectionreservoir comprising water and an electrolyte, and to the area of theelectrode subassembly; and (2) as a counter electrode to the firstsensing electrode at which the chemical compound is catalyticallyconverted at the face of the sensing electrode to produce an electricalsignal.

The reference (FIGS. 5, 544 and 545; FIG. 4, 432) and sensing electrodes(FIGS. 5, 542 and 543; FIG. 4, 431), as well as, the bimodal electrode(FIGS. 5, 540 and 541; FIG. 4, 430) are connected to a standardpotentiostat circuit during sensing. In general, practical limitationsof the system require that the bimodal electrode will not act as both acounter and iontophoretic electrode simultaneously.

The general operation of an iontophoretic sampling system is thecyclical repetition of two phases: (1) a reverse-iontophoretic phase,followed by a (2) sensing phase. During the reverse iontophoretic phase,the first bimodal electrode (FIG. 5, 540) acts as an iontophoreticcathode and the second bimodal electrode (FIG. 5, 541) acts as aniontophoretic anode to complete the circuit. Analyte is collected in thereservoirs, for example, a hydrogel (FIGS. 5, 547 and 548). At the endof the reverse iontophoretic phase, the iontophoretic current is turnedoff. During the sensing phase, in the case of glucose, a potential isapplied between the reference electrode (FIG. 5, 544) and the sensingelectrode (FIG. 5, 542). The chemical signal reacts catalytically on thecatalytic face of the first sensing electrode (FIG. 5, 542) producing anelectrical current, while the first bi-modal electrode (FIG. 5, 540)acts as a counter electrode to complete the electrical circuit.

At the end of the sensing phase, the next iontophoresis phase begins.The polarity of the iontophoresis current is reversed in this cyclerelative to the previous cycle, so that the first bi-modal electrode(FIG. 5, 540) acts as an iontophoretic anode and the second bi-modalelectrode (FIG. 5, 541) acts as an iontophoretic cathode to complete thecircuit. At the end of the iontophoretic phase, the sensor is activated.The chemical signal reacts catalytically on the catalytic face of thesecond sensing electrode (FIG. 5, 543) producing an electrical current,while the second bi-modal electrode (FIG. 5, 541) acts as a counterelectrode to complete the electrical circuit.

The iontophoretic and sensing phases repeat cyclically with the polarityof the iontophoretic current alternating between each cycle. Thisresults in pairs of readings for the signal, that is, one signalobtained from a first iontophoretic and sensing phase and a secondsignal obtained from the second phase. These two values can be used (i)independently as two signals, (ii) as a cumulative (additive) signal, or(iii) the signal values can be added and averaged.

If two active reservoirs are used for analyte detection (for example,where both hydrogels contain the GOx enzyme), a sensor consistency checkcan be employed that detects whether the signals from the reservoirs arechanging in concert with one another. This check compares the percentagechange from the calibration signal for each reservoir, then calculatesthe difference in percentage change of the signal between the tworeservoirs. If this difference is greater than a predetermined thresholdvalue (which is commonly empirically determined), then the signals aresaid not to be tracking one another and the data point related to thetwo signals can be, for example, ignored.

The electrode described is particularly adapted for use in conjunctionwith a hydrogel collection reservoir system for monitoring glucoselevels in a subject through the reaction of collected glucose with theenzyme glucose oxidase present in the hydrogel matrix.

The bi-modal electrode is preferably comprised of Ag/AgCl. Theelectrochemical reaction which occurs at the surface of this electrodeserves as a facile source or sink for electrical current. This propertyis especially important for the iontophoresis function of the electrode.Lacking this reaction, the iontophoresis current could cause thehydrolysis of water to occur at the iontophoresis electrodes causing pHchanges and possible gas bubble formation. The pH changes to acidic orbasic pH could cause skin irritation or burns. The ability of an Ag/AgClelectrode to easily act as a source of sink current is also an advantagefor its counter electrode function. For a three electrodeelectrochemical cell to function properly, the current generationcapacity of the counter electrode must not limit the speed of thereaction at the sensing electrode. In the case of a large sensingelectrode, the ability of the counter electrode to sourceproportionately larger currents is required.

The design of the sampling system provides for a larger sensingelectrode (see for example, FIG. 4) than previously designed.Consequently, the size of the bimodal electrode must be sufficient sothat when acting as a counter electrode with respect to the sensingelectrode the counter electrode does not become limiting the rate ofcatalytic reaction at the sensing electrode catalytic surface.

Two methods exist to ensure that the counter electrode does not limitthe current at the sensing electrode: (1) the bi-modal electrode is mademuch larger than the sensing electrode, or (2) a facile counter reactionis provided.

During the reverse iontophoretic phase, the power source provides acurrent flow to the first bi-modal electrode to facilitate theextraction of the chemical signal into the reservoir. During the sensingphase, the power source is used to provide voltage to the first sensingelectrode to drive the conversion of chemical signal retained inreservoir to electrical signal at the catalytic face of the sensingelectrode. The power source also maintains a fixed potential at theelectrode where, for example hydrogen peroxide is converted to molecularoxygen, hydrogen ions, and electrons, which is compared with thepotential of the reference electrode during the sensing phase. While onesensing electrode is operating in the sensing mode it is electricallyconnected to the adjacent bimodal electrode which acts as a counterelectrode at which electrons generated at the sensing electrode areconsumed.

The electrode sub-assembly can be operated by electrically connectingthe bimodal electrodes such that each electrode is capable offunctioning as both an iontophoretic electrode and counter electrodealong with appropriate sensing electrode(s) and reference electrode(s),to create standard potentiostat circuitry.

A potentiostat is an electrical circuit used in electrochemicalmeasurements in three electrode electrochemical cells. A potential isapplied between the reference electrode and the sensing electrode. Thecurrent generated at the sensing electrode flows through circuitry tothe counter electrode (i.e., no current flows through the referenceelectrode to alter its equilibrium potential). Two independentpotentiostat circuits can be used to operate the two biosensors. For thepurpose of the present sampling system, the electrical current measuredat the sensing electrode subassembly is the current that is correlatedwith an amount of chemical signal.

With regard to continual operation for extended periods of time, Ag/AgClelectrodes are provided herein which are capable of repeatedly forming areversible couple which operates without unwanted electrochemical sidereactions (which could give rise to changes in pH, and liberation ofhydrogen and oxygen due to water hydrolysis). The Ag/AgCl electrodes ofthe present sampling system are thus formulated to withstand repeatedcycles of current passage in the range of about 0.01 to 1.0 mA per cm²of electrode area. With regard to high electrochemical purity, theAg/AgCl components are dispersed within a suitable polymer binder toprovide an electrode composition which is not susceptible to attack(e.g., plasticization) by components in the collection reservoir, e.g.,the hydrogel composition. The electrode compositions are also formulatedusing analytical- or electronic-grade reagents and solvents, and thepolymer binder composition is selected to be free of electrochemicallyactive contaminants which could diffuse to the biosensor to produce abackground current.

Since the Ag/AgCl iontophoretic electrodes must be capable of continualcycling over extended periods of time, the absolute amounts of Ag andAgCl available in the electrodes, and the overall Ag/AgCl availabilityratio, can be adjusted to provide for the passage of high amounts ofcharge. Although not limiting in the sampling system described herein,the Ag/AgCl ratio can approach unity. In order to operate within thepreferred system which uses a biosensor having a geometric area of 0.1to 3 cm², the iontophoretic electrodes are configured to provide anapproximate electrode area of 0.3 to 1.0 cm², preferably about 0.85 cm².These electrodes provide for reproducible, repeated cycles of chargepassage at current densities ranging from about 0.01 to 1.0 mA/cm² ofelectrode area. More particularly, electrodes constructed according tothe above formulation parameters, and having an approximate electrodearea of 0.85 cm², are capable of a reproducible total charge passage (inboth anodic and cathodic directions) of 270 mC, at a current of about0.3 mA (current density of 0.35 mA/cm²) for 48 cycles in a 24 hourperiod.

Once formulated, the Ag/AgCl electrode composition is affixed to asuitable rigid or flexible nonconductive surface as described above withrespect to the biosensor electrode composition. A silver (Ag) underlayeris first applied to the surface in order to provide uniform conduction.The Ag/AgCl electrode composition is then applied over the Ag underlayerin any suitable pattern or geometry using various thin film techniques,such as sputtering, evaporation, vapor phase deposition, or the like, orusing various thick film techniques, such as film laminating,electroplating, or the like. Alternatively, the Ag/AgCl composition canbe applied using screen printing, pad printing, inkjet methods, transferroll printing, or similar techniques. Preferably, both the Ag underlayerand the Ag/AgCl electrode are applied using a low temperature screenprint onto a polymeric substrate. This low temperature screen print canbe carried out at about 125 to 160° C., and the screening can be carriedout using a suitable mesh, ranging from about 100-400 mesh.

In another preferred embodiment, the automatic sampling systemtransdermally extracts the sample in a continual manner over the courseof a 1-24 hour period, or longer, using sonophoresis. More particularly,a source of ultrasonic radiation is coupled to the collection reservoirand used to provide sufficient perturbation of the target tissue surfaceto allow passage of the analyte (glucose) across the tissue surface. Thesource of ultrasonic radiation provides ultrasound frequencies ofgreater than about 10 MHz, preferably in the range of about 10 to 50MHz, most preferably in the range of about 15 to 25 MHz. It should beemphasized that these ranges are intended to be merely illustrative ofthe preferred embodiment; in some cases higher or lower frequencies maybe used.

The ultrasound may be pulsed or continuous, but is preferably continuouswhen lower frequencies are used. At very high frequencies, pulsedapplication will generally be preferred so as to enable dissipation ofgenerated heat. The preferred intensity of the applied ultrasound isless than about 5.0 W/cm², more preferably is in the range of about 0.01to 5.0 W/cm², and most preferably is in the range of 0.05 to 3.0 W/cm².

Virtually any type of device may be used to administer the ultrasound,providing that the device is capable of producing the suitable frequencyultrasonic waves required by the sampling system. An ultrasound devicewill typically have a power source such as a small battery, atransducer, and a means to attach the system to the sampling systemcollection reservoir. Suitable sonophoresis sampling systems aredescribed in International Publication No. WO 91/12772, published 5 Sep.1991, the disclosure of which is incorporated herein by reference.

As ultrasound does not transmit well in air, a liquid medium isgenerally needed in the collection reservoir to efficiently and rapidlytransmit ultrasound between the ultrasound applicator and the tissuesurface.

Referring now to FIG. 3, an exploded view of the key components from apreferred embodiment of an autosensor is presented. The sampling systemcomponents include two biosensor/iontophoretic electrode assemblies, 304and 306., each of which have an annular iontophoretic electrode.,respectively indicated at 308 and 310, which encircles a biosensor 312and 314. The electrode assemblies 304 and 306 are printed onto apolymeric substrate 316 which is maintained within a sensor tray 318. Acollection reservoir assembly 320 is arranged over the electrodeassemblies, wherein the collection reservoir assembly comprises twohydrogel inserts 322 and 324 retained by a gel retaining layer 326.

Referring now to FIG. 9, an exploded view of the key components fromanother embodiment of an autosensor for use in an iontophoretic samplingdevice is presented. The sampling system components include, but are notlimited to, the following: a sensor-to-tray assembly comprising twobimodal electrode assemblies and a support tray 904; two holes 906 toinsure proper alignment of the support tray in the sampling device; aplowfold liner 908 used to separate the sensors from the hydrogels 912(for example, during storage); a gel retaining layer 910; a mask layer914 (where the gel retaining layer, hydrogels, and mask layer form acollection assembly, which can, for example, be a laminate); and apatient liner 916.

The components shown in exploded view in FIGS. 3 and 9 are intended foruse in, for example, an automatic sampling device which is configured tobe worn like an ordinary wristwatch. As described in InternationalPublication No. Wo 96/00110, published 4 Jan. 1996, the wristwatchhousing (not shown) contains conductive leads which communicate with theiontophoretic electrodes and the biosensor electrodes to control cyclingand provide power to the iontophoretic electrodes, and to detectelectrochemical signals produced at the biosensor electrode surfaces.The wristwatch housing can further include suitable electronics (e.g.,microprocessor, memory, display and other circuit components) and powersources for operating the automatic sampling system.

Modifications and additions to the embodiments of FIGS. 3 and 9 will beapparent to those skilled in the art in light of the teachings of thepresent specification. The laminates and collection assemblies describedherein are suitable for use as consumable components in an iontophoreticsampling device.

In one aspect, the electrode assemblies can include bimodal electrodesas shown in FIG. 4 and described above.

Modifications and additions to the embodiments shown in FIGS. 3 and 9will be apparent to those skilled in the art.

2.2.0 Converting to an Analyte-Specific Value.

The raw signal is then converted into an analyte-specific value using acalibration step which correlates the signal obtained from the sensingdevice with the concentration of the analyte present in the biologicalsystem. A wide variety of calibration techniques can be used tointerpret such signals. These calibration techniques apply mathematical,statistical and/or pattern recognition techniques to the problem ofsignal processing in chemical analyses, for example, using neuralnetworks, genetic algorithm signal processing, linear regression,multiple-linear regression, or principal components analysis ofstatistical (test) measurements.

One method of calibration involves estimation techniques. To calibratean instrument using estimation techniques, it is necessary to have a setof exemplary measurements with known concentrations referred to as thecalibration set (e.g., reference set). This set consists of S samples,each with m instrument variables contained in an S by m matrix (X), andan S by 1 vector (y), containing the concentrations. If a prioriinformation indicates the relationship between the measurement andconcentration is linear, the calibration will attempt to determine an Sby 1 transformation or mapping (b), such that y=Xb, is an optimalestimate of y according to a predefined criteria. Numerous suitableestimation techniques useful in the practice of the invention are knownin the art. These techniques can be used to provide correlation factors(e.g., constants), which correlation factors are then used in amathematical transformation to obtain a measurement value indicative ofthe concentration of analyte present in the biological system at thetimes of measurement.

In one particular embodiment, the calibration step can be carried outusing artificial neural networks or genetic algorithms. The structure ofa particular neural network algorithm used in the practice of theinvention can vary widely; however, the network should contain an inputlayer, one or more hidden layers, and one output layer. Such networkscan be trained on a test data set, and then applied to a population.There are an infinite number of suitable network types, transferfunctions, training criteria, testing and application methods which willoccur to the ordinarily skilled artisan upon reading the instantspecification.

The iontophoretic glucose sampling device described hereinabovetypically uses one or more “active” collection reservoirs (e.g., eachcontaining the GOx enzyme) to obtain measurements. In one embodiment,two active collection reservoirs are used. An input value can beobtained from these reserviors by, for example, taking an averagebetween signals from the reservoirs for each measurement time point orusing a summed value. Such inputs are discussed in greater detail below.In another embodiment, a second collection reservoir can be providedwhich does not contain, for example, the GOx enzyme. This secondreservoir can serve as an internal reference (blank) for the sensingdevice, where a biosensor is used to measure the “blank” signal from thereference reservoir which signal can then be used in, for example, ablank subtraction step.

In the context of such a sampling device an algorithm, in a preferredembodiment a Mixtures of Experts algorithm, could use the followinginputs to provide a blood glucose measurement: time (for example, timesince monitor was applied to a subject, and/or time since calibration);signal from an active reservoir; signal from a blank reservoir; averaged(or a cumulative) signal from two active reservoirs; calibration time;skin temperature; voltage; normalized background; raw data current; peakor minimum value of a selected input, e.g., current, averaged signal,calibrated signal; discrete value points of a selected input, e.g.,current, averaged signal, calibrated signal; integral averagetemperature, initial temperature, or any discrete time temperature; skinconductivity, including, but not limited to, sweat value, iontophoreticvoltage, baseline value, normalized baseline value, other backgroundvalues; relative change in biosensor current or iontophoretic voltage(relative to calibration) as an indicator of decay; alternateintegration ranges for calculating nanocoulomb (nC) values, e.g., usingan entire biosensor time interval, or alternative ranges of integration(for example, using discrete time points instead of ranges, break outintervals from the total sampling time interval, or full integration ofthe interval plus partial integration of selected portions of theinterval); and, when operating in the training mode, measured glucose(use of exemplary inputs are presented in Examples 1 and 2). Further, acalibration ratio check is described in Example 4 that is useful toinsure that the calibration has been efficacious, and that thecalibration demonstrates a desired level of sensitivity of the samplingsystem.

2.3.0 Predicting Measurements

The analyte-specific values obtained using the above techniques are usedherein to predict target analyte concentrations in a biological systemusing a Mixtures of Experts (MOE) analysis.

The Mixtures of Experts algorithm breaks up a non-linear predictionequation into several linear prediction equations (“Experts”). An“Expert” routine is then used to switch between the different linearequations. In the equations presented below, the w (weighting) factordetermines the switch by weighting the different Experts with a numberbetween 0 and 1, with the restriction that:

${\sum\limits_{i = 1}^{n}w_{i}} = 1$

The Mixtures of Experts algorithm of the present invention is based onthe ideal case presented in Equation 1, where the individual expertshave a linear form:

$\begin{matrix}{{An} = {\sum\limits_{i = 1}^{n}{{An}_{i}w_{i}}}} & (1)\end{matrix}$

wherein (An) is an analyte of interest, n is the number of experts,An_(i) is the analyte predicted by Expert i; and w_(i) is a parameter.The number of experts is chosen based on the quality of the fit of themodel, subject to the requirement that it is desirable to use the leastnumber of experts possible. The number of experts is preferably lessthan 100, and more preferably less than 30. In most cases, selection ofthe fewest possible experts is desirable.

The individual Experts An_(i) are further defined by the expressionshown as Equation (2).

$\begin{matrix}{{An}_{i} = {{\sum\limits_{j = 1}^{m}{a_{ij}P_{j}}} + z_{i}}} & (2)\end{matrix}$

wherein, An_(i) is the analyte predicted by Expert i; P_(j) is one of mparameters, m is typically less than 100; a_(ij) are coefficients; andz_(i) is a constant.

The weighting value, w_(i), is defined by the formula shown as Equation(3).

$\begin{matrix}{w_{i} = \frac{^{d_{i}}}{\left\lbrack {\sum\limits_{k = 1}^{n}^{d_{k}}} \right\rbrack}} & (3)\end{matrix}$

where e refers to the exponential function and the d_(k) (note that thed_(i) in the numerator of Equation 3 is one of the d_(k)) are aparameter set analogous to Equation 2 that is used to determine theweights w_(i). The d_(k) are given by Equation 4.

$\begin{matrix}{d_{k} = {{\sum\limits_{j = 1}^{m}{\alpha_{jk}P_{j}}} + \omega_{k}}} & (4)\end{matrix}$

where α_(jk) is a coefficient, P_(j) is one of m parameters, and whereω_(k) is a constant.

The Mixtures of Experts method described by the above equations issupplied with a large data base of empirically obtained informationabout the parameters defined by the equations. By employing a linearregression function, the equations are simultaneously solved for thevalues of all coefficients and constants. In other words, the algorithmis trained to be predictive for the value of An (the analyte) given aparticular set of data. A preferred optimization method to determine thecoefficients and constants is the Expectation Maximization method(Dempster, A. P., N. M. Laird, and D. B. Rubin, J. Royal StatisticalSociety (Series B-Methodological) 39:(1), 1977). Other optimizationmethods include the Levenburg-Marquardt algorithm (Marquardt, D. W., J.Soc. Ind. Appl. Math. 11:p 431-441, 1963) and the Simplex algorithm(Nelder, J. A., and Mead, R., Computer Journal 7:p 308, 1965).

In the context of blood glucose monitoring with an iontophoreticsampling device, the MOE algorithm allows for the accurate prediction ofglucose concentration. In this regard, during a typical iontophoreticmeasuring cycle, iontophoretic extraction of the analyte is carried outfor a suitable amount of time, for example about 1 to 30 minutes, afterwhich time the extracted analyte is detected for a suitable amount oftime, for example about 1-30 minutes. An application of the Mixtures ofExperts algorithm to a specific set of parameters for glucose monitoringis presented in Example 1.

In the context of blood glucose monitoring with an iontophoreticsampling device, the Mixtures of Experts algorithm allows for theaccurate prediction of blood glucose concentrations.

2.4.0 Algorithm Modifications

A further aspect of the present invention is the modification of theMixtures of Experts (MOE) algorithm. The MOE can be modified in a numberof ways including, but not limited to, the following modifications:using different groups of selected inputs (see above); adapting thealgorithm by modifying the training set; using different algorithms ormodifications of the MOE for different ranges of analyte detection;using different statistical distributions in the Mixtures of Experts;rejection of selected expert(s); and, switching algorithms.

2.4.1 Adapting the Algorithm

The Mixtures of Experts (MOE) is trained using sets of data that containpatterns. Those patterns, represented in a training data set, typicallygive good performance. Accordingly, training MOE with a wide variety ofpatterns improves the predictive performance of MOE, for example, usinga variety of blood glucose patterns that occur in diabetics patients toobtain parameters that represent the patterns. In this case the selectedpatterns are used to develop an appropriate training set for MOE andthen the parameters generated from that training set are used to testdata representing a variety of patterns. In one embodiment, a “global”training set may be augmented by providing a training data set developedfrom an individual subject's blood glucose data taken over several (ormany) days. Such an individual pattern is potentially useful tocustomize the algorithm to that subject. The parameters generated fromusing a training set including such an individual patterns is thentested in the same individual to determine whether the expanded trainingdata set provides better predicted values. In an alternative embodiment,a selected percentage of the global training set can be used with theindividual's training set (rather than using the entire global trainingset).

Further, the data comprising a training data set can be specificallychosen to optimize performance of the MOE under specific conditions.Such optimization may include, for example, using diverse data sets orselecting the best data to represent a specific condition. For example,different training data sets based on data obtained from a variety ofraces can be used to train the MOE to optimize predictive performancefor individual members of the different races represented by differentdata sets.

Finally, MOE is typically trained with values chosen in a selected range(e.g., blood glucose values in the range of 40-400 mg/dl). However, theMOE can be trained with data sets that fall outside of the selectedrange.

2.4.2 Algorithm Optimized for Different Ranges

The MOE can be optimized for predictive performance in selected rangesof data. Depending on the range different MOEs may be invoked forprediction of analyte values (see “Switching Algorithms” below).Alternatively, different algorithms can be used for prediction of valuesin selected ranges of analyte detection. For example, MOE may be usedfor prediction of glucose values in a range of 40-400 mg/dl; however, atlow and high ends of glucose values a specifically defined function canbe applied to the data in order to get preferred values. Such preferredvalues may, for example, be useful in the situation whereunder-prediction is more desirable than over-prediction (e.g., at lowblood glucose values). In this case a modification of MOE may be used oran specific algorithm may be optimized for prediction in the selectedrange using, for example, a non-linear distribution function thatemphasizes predicting low blood glucose (BG) in the range BG≦100.

2.4.3 Employing Different Distribution Functions

When calculating the weights used in the MOE algorithm a selecteddistribution is used. One exemplary distribution is a Gaussiandistribution (Example 3) that weighs deviations relative to the squareof difference from the mean. However, other distributions can be used toimprove predictive function of the algorithm. For example, a Laplaciandistribution function was used in the calculations presented in Example4. The Laplacian distribution has longer tails than a Gaussiandistribution, and weighs deviations relative to the absolute differencefrom the mean. Other distribution functions can be used as wellincluding, but not limited to, Cauchy distribution or a specificdistribution function devised (or calculated) based on specific datasets obtained, for example, from different individuals or differentgroups of individuals (e.g., different races).

2.4.4 Rejecting Experts

When multiple experts are used in the MOE each expert can be inspectedto determine if, for example, one or more of the experts is providingincongruous values. When such an expert is identified (e.g., in thecalculation of a particular data point) the expert may be eliminated forthat calculation and the weights of the remaining experts readjustedappropriately. Inspection of the experts can be carried out by aseparate algorithm and can, for example, be based on whether the valuepredicted by the expert falls outside of a designated range. If thevalue falls outside of a designated range, the expert may be eliminatedin that calculation. For example, Example 3 describes the use of threeexperts (BG₁, BG₂, and BG₃) in an MOE for prediction of blood glucosevalues, wherein a weighted average is used to calculate the final bloodglucose value. However, each of these three experts can be inspected todetermine if one (or more) of them does not make sense (e.g., isproviding a stochastic or out-lying value significantly different fromthe other two experts). The expert providing the incongruous value isdisregarded and the weights of the other two experts are readjustedaccordingly.

2.4.5 Switching Algorithms

In yet another aspect of the present invention, prediction of theconcentration of an analyte can be accomplished using specializedalgorithms, where the specialized algorithms are useful for predictionsin particular situations (e.g., particular data sets or ranges ofpredicted values) and where the algorithm used for performing thecalculations is determined based on the situation. In this case a“switch” can be used to employ one (or more) algorithm rather thananother (or more) algorithm. For example, a global MOE algorithm can bethe switch used to selected one of three different MOE algorithms. Inone embodiment such a global MOE algorithm may be used to determine ablood glucose value. The blood glucose value is determined, by thealgorithm, to fall into one of three ranges (for example, low, normal,and high). For each range there is an separate MOE algorithm thatoptimizes the prediction for values in the particular range. The globalMOE algorithm then selects the appropriate MOE algorithm based on thevalue and the selected MOE performs a new prediction of blood glucosevalues based on the original input values but optimized for the rangeinto which the value was predicted (by the global MOE) to fall. As afurther illustration, inputs to determine a blood glucose value areprovided to a global MOE which determines that the value is a low-value.The inputs are then directed to a Low-Value Optimized MOE to generate amore accurate predicted blood glucose value.

Specialized algorithms may be developed to be used in different parts ofa range of analyte signal spectrum or other input values (e.g., highsignal/low signal; high BGCal/low BGCal; high/low calratio; high/lowtemp; etc., for all variables used in the prediction). A globalalgorithm can be used to decide which region of the spectrum the analytesignal is in, and then the global algorithm switches the data to theappropriate specialized algorithm.

In another embodiment, an algorithm other than the MOE can be used asthe switch to choose among a set of MOE algorithms, or an MOE can beused as the switch to choose among a set of other algorithms. Further,there can be multiple levels of specialized switching (which can begraphically represented for instance by branched tree-diagrams).

Following here are several specific, non-limiting examples, of the usesof switching in the practice of the present invention when blood glucosevalues are being determined.

In one embodiment, variables are identified that explicitly representsignal decay, for example, a switch based on elapsed time sincecalibration (early or late) or the value of Calratio at CAL (high orlow). An exemplary switch of this type is represented by elapsed timesince calibration where, for example, the algorithm described in Example3 may be trained independently with inputs from an early phase of sensoruse and inputs from a late phase sensor use (e.g., the total useful lifeof a sensor element may be split into two-halves—early and late). Then,depending on the time since calibration that selected input values arebeing obtained (an exemplary switch), the input values are directed toan MOE algorithm that was trained on data from the appropriate phase(i.e., either early or late). Such a switch is useful to help correctfor error based in sensor decay.

Another exemplary switch of this type is represented by the value ofCalratio at the calibration point. Calratio is described in Example 4.The Calratio is a measure of sensor sensitivity. Accordingly, if desiredthe Calratio range can be divided into two halves (high and low ranges).The algorithm described in Example 3 may be trained independently withinputs from the high and low ranges of the Calratio. A switch is thenbased on the Calratio values to direct the inputs to the MOE algorithmthat is trained with the appropriate data set (i.e., data setscorresponding to inputs from high and low Calratio ranges).

2.5.0 Decreasing the Bias of a Data Set

In addition to the MOE algorithm described in the present specification,following here is a description of a method to alter data used togenerate a training data set so as to correct slope, intercept (andresultant bias) introduced by the limited range of data input. Thisinvention provides a useful correction for any asymmetric data inputthat gives a bias to resultant predictions. In this method, the valuesof a data set are used to create a second data set that mirrors thefirst, i.e., positive values become negative values (opposite signs).The two data sets are then used as the training data set. Thistransformation of the asymmetrical data set results in a forced symmetryof the data comprising the training set.

The following is a non-limiting example of this method for thecorrection of bias using blood glucose level determination. In the bloodglucose value determinations described herein there is an inherent bias(manifested by a slope of <1 and a positive intercept, e.g., FIG. 10A;in the figure, pBG is predicted blood glucose and mBG is directlymeasured blood glucose—measured, for example, using a HemoCue® meter)introduced into the prediction function. This is in part due to the factthat there are no blood glucose levels of <40 mg/dl used in the datainput training set. The data input for training the MOE algorithm, usedto predict blood glucose levels, uses, for example, the followingvariables: elapsed time since calibration, average signal, calibratedsignal, and the blood glucose at the calibration point (see, e.g.,Examples 3 and 4). The value that these inputs predict and try to matchis directly measured blood glucose. The allowed range for blood glucoseis 40-400 mg/dl. Due to this limited range of blood glucose, theresultant function predictions (i.e., via the MOE) result in an inherentbias, slope <1 and positive intercept when plotting predicted bloodglucose (y-axis variable, pBG, FIG. 10A) versus directly measured bloodglucose (x-axis variable, mBG, FIG. 10A).

The method of the present invention circumvents this problem byaugmenting the original input data set with a data set comprising thesame elapsed time since calibration, but with values of the averagesignal (in nanocoulombs) and directly measured blood glucose both of theopposite sign relative to the original, real data set. The calibratedsignal is then calculated using the opposite sign data. In this way theinput data is doubled and is now symmetric around the origin (FIG. 10B;in the figure, pBG is predicted blood glucose and mBG is directlymeasured blood glucose—measured, for example, using a HemoCue® meter).In FIG. 10B the dotted lines represent the slopes predicted from thesingle data set with which they are associated. The solid line betweenthe two dashed lines represents the corrected slope based on use of theoriginal data set and the opposite sign data set to train the algorithm.

The value of this approach when plotting predicted blood glucose (usingMOE) versus measured blood glucose can be seen by examining the resultspresented in the following table.

Original Data Set & Opposite Sign Original Data Set Data Set DemingSlope* 0.932 1.042 Deming Intercept* 12.04 −5.63 Bias 50 mg/dl 8.64−3.53 Bias 80 mg/dl 6.6 −2.27 Bias 100 mg/dl 5.24 −1.43 Bias 150 mg/dl1.84 0.67 Bias 200 mg/dl −1.56 2.77 *Based on orthogonal regression witha variance ratio equal to two.

As the results in this table demonstrate, the bias reducing method ofthe present invention has a slope closer to 1, an intercept closer tozero, and the bias values are, in general, closer to zero.

Accordingly, one aspect of the present invention is a method fordecreasing the bias of a data set. The method involves generating asecond data set that has values opposite in sign of the original dataset and using this first and second data set as a combined data set totrain the algorithm (e.g., MOE).

EXAMPLES

The following examples are put forth so as to provide those of ordinaryskill in the art with a complete disclosure and description of how tomake and use the devices, methods, and formulae of the presentinvention, and are not intended to limit the scope of what the inventorregards as the invention. Efforts have been made to ensure accuracy withrespect to numbers used (e.g., amounts, temperature, etc.) but someexperimental errors and deviations should be accounted for. Unlessindicated otherwise, parts are parts by weight, molecular weight isweight average molecular weight, temperature is in degrees Centigrade,and pressure is at or near atmospheric.

Example 1 Application of the “Mixtures of Experts” to Glucose Monitoring

This example describes the use of a Mixtures of Experts (MOE) algorithmto predict blood glucose data from a series of signals.

In the present example, a GlucoWatch® monitor was used to collect dataand the following variables were chosen to generate data sets for theMOE algorithm:

1) elapsed time (time), elapsed time since the GlucoWatch® monitor wasapplied to the subject, i.e., elapsed time since the sampling system wasplaced in operative contact with the biological system;

2) active signal (active), in this example, the value of the activeparameter corresponded to the nanoamp signal that was integrated overthe sensing time-interval to give the active parameter in nanocoulombs(nC);

3) calibrated signal (signal), in this example was obtained bymultiplying an active by a constant, where the constant was defined asthe blood glucose level at the calibration point divided by the activevalue at the calibration point. For example, as follows:

${signal} = {\frac{{BG}/{cp}}{{active}/{cp}}({active})}$

where the slope of the line active versus blood glucose had a non-zerointercept and the offset took into account that the intercept was notzero. In the alternative, the constant could be as follows:

${signal} = {\frac{{BG}/{cp}}{\left( {{{active}/{cp}} + {offset}} \right)}\left( {{active} + {offset}} \right)}$

where the offset takes into account the intercept value.

4) blood glucose value at the calibration point (BG/cp) was determinedby direct blood testing.

Other possible variables include, but are not limited to, temperature,iontophoretic voltage (which is inversely proportional to skinresistance), and skin conductivity.

Large data sets were generated by collecting signals using a transdermalsampling system that was placed in operative contact with the skin. Thesampling system transdermally extracted the analyte from the biologicalsystem using an appropriate sampling technique (in this case,iontophoresis). The transdermal sampling system was maintained inoperative contact with the skin to provide a near continual orcontinuous stream of signals.

The basis of the Mixtures of Experts was to break up a non-linearprediction equation (Equation 5, below) into several Expert predictionequations, and then to have a routine to switch between the differentlinear equations. For predicting blood glucose levels, three separatelinear equations (Equations 6, 7, and 8) were used to represent bloodglucose, with the independent variables discussed above of time, active,signal, blood glucose at a calibration point (BG/cp), and a constant(t_(i)).

The switching between equations 6, 7, and 8 was determined by theparameters w₁, w₂, and w₃ in equation 5, which was further determined bythe parameters d₁, d₂, and d₃ as given by equations 9-14, where theindividual experts had a linear form:

BG=w ₁ BG ₁ +w ₂ BG ₂ +w ₃ BG ₃  (5)

wherein (BG) was blood glucose, there are three experts (n=3); BG₁ wasthe analyte predicted by Expert i; and w_(i) was a parameter, and theindividual Experts BG_(i) were further defined by the expression shownas Equations 6, 7, and 8

BG ₁ =p ₁(time)+q ₁(active)+r ₁(signal)+s ₁(BG|cp)+t ₁  (6)

BG ₂ =p ₂(time)+q ₂(active)+r ₂(signal)+s ₂(BG|cp)+t ₂  (7)

BG ₃ =p ₃(time)+q ₃(active)+r ₃(signal)+s ₃(BG|cp)+t ₃  (8)

wherein, BG_(i) was the analyte predicted by Expert i; parametersinclude, time (elapsed time), active (active signal), signal (calibratedsignal), and BG/cp (blood glucose value at a calibration point); p_(i),q_(i), r_(i), and s_(i) were coefficients; and t_(i) was a constant; andfurther where the weighting value, w_(i), was defined by the formulasshown as Equations 9, 10, and 11

$\begin{matrix}{w_{1} = \frac{^{d_{1}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (9) \\{w_{2} = \frac{^{d_{2}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (10) \\{w_{3} = \frac{^{d_{3}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (11)\end{matrix}$

where e referred to the exponential function and d_(i) was a parameterset (analogous to Equations 6, 7, and 8) that were used to determine theweights w_(i), given by Equations 9, 10, and 11, and

d ₁=τ₁(time)+β₁(active)+γ₁(signal)+δ₁(BG|cp)+∈₁  (12)

d ₂=τ₂(time)+β₂(active)+γ₂(signal)+δ₂(BG|cp)+∈₂  (13)

d ₃=τ₃(time)+β₃(active)+γ₃(signal)+δ₃(BG|cp)+∈₃  (14)

where τ_(i), β_(i), γ_(i) and δ_(i) were coefficients, and where ∈_(i)is a constant.

To calculate the above parameters an optimization method was applied tothe algorithm (Equations 5-14) and the large data set. The optimizationmethod used was the Expectation Maximization method (Dempster, A. P., N.M. Laird, and D. B. Rubin, J. Royal Statistical Society (SeriesB-Methodological) 39:(1), 1977), but other methods may be used as well.

The parameters in these equations were determined such that theposterior probability of the actual glucose was maximized.

Example 2 Prediction of Measurement Values I

Iontophoretic extraction of glucose was carried out using a GlucoWatch®monitor which employs (i) a low-level iontophoretic current to extractglucose through patient's skin, and (ii) an electrochemical biosensor todetect the extracted glucose. Iontophoresis was carried out for 3 minuteintervals and electrochemical detection was carried out for 7 minuteintervals to result in 10 minute measurement cycles—thus generatingcollections of data (data sets) as described in Example 1.

The data that were used for this analysis were obtained by diabeticsubjects each wearing a GlucoWatch® monitor over a 14 hour period. TheMOE inputs consisted of the following parameters (described in Example1): time, active, signal, blood glucose at a calibration point (BG/cp).These training data were used to determine the unknown parameters in theMOE using the Expectation Maximization Method. The output of the MOEalgorithm was the measured value of blood glucose. Using a three hourtime point for calibrating the GlucoWatch® monitor, the mean percentageerror (MPE) between the actual blood glucose and the calculated (MOEpredicted) blood glucose was 13%.

In a diabetic study consisting of 61 patients, the diabetic subjects'blood glucose ranged from 23-389 mg/dl. A protocol was followed wherebya subject (who had fasted since the previous midnight) came to a testsite where the GlucoWatch® monitor was applied to the subject, started,and calibrated. Over the next 14 hours, the subject had normal meals anda finger prick blood sample was taken every 20 minutes for glucosedetermination (“actual glucose”). Blood glucose levels were measuredusing the HemoCue® meter (HemoCue AB, Sweden), which has an accuracy of±10%.

A plot of the glucose levels predicted by the Mixtures of Expertsalgorithm (based on the data described above) versus the actual bloodglucose levels is presented in FIG. 6 (a Correlation Plot). Analysis ofthe data shown in FIG. 6 showed a slope of 0.88, an intercept of 14, anda correlation coefficient of R=0.93. There were N=1,348 pointscomprising the Correlation Plot.

These statistical results, along with the MPE=0.13 (discussed above),show the excellent predictive capabilities of the GlucoWatch® monitorand the Mixtures of Experts algorithm.

Example 3

Another Application of the “Mixtures of Experts” to Glucose Monitoring

This example describes the use of a Mixtures of Experts (MOE) algorithmto predict blood glucose data from a series of signals.

In the present example, a GlucoWatch® monitor was used to collect dataand the following variables were chosen to generate data sets for theMOE algorithm:

1) time since calibration (time_(c)), the elapsed time since thecalibration step was carried out for the GlucoWatch® monitor (in hours);

2) active signal (active), in this example, the value of the activeparameter corresponded to the averaged signal from two activereservoirs, where each reservoir provided a nanoamp signal that wasintegrated over the sensing time-interval, the two values were thenadded and averaged to give the active parameter in nanocoulombs (nC);

3) calibrated signal (signal), in this example was obtained as follows:

${signal} = {\frac{{BG}/{cp}}{\left( {{{active}/{cp}} + {offset}} \right)}\left( {{active} + {offset}} \right)}$

where the offset takes into account the intercept value.

4) blood glucose value at the calibration point (BG/cp), in mg/dl, wasdetermined by direct blood testing.

Other possible variables include, but are not limited to, temperature,iontophoretic voltage (which is inversely proportional to skinresistance), and skin conductivity.

Large data sets were generated by collecting signals using a transdermalsampling system that was placed in operative contact with the skin. Thesampling system transdermally extracted the analyte from the biologicalsystem using an appropriate sampling technique (in this case,iontophoresis). The transdermal sampling system was maintained inoperative contact with the skin to provide a near continual orcontinuous stream of signals.

The basis of the Mixtures of Experts was to break up a non-linearprediction equation (Equation 15, below) into several Expert predictionequations, and then to have a routine to switch between the differentlinear equations. For predicting blood glucose levels, three separatelinear equations (Equations 16, 17, and 18) were used to represent bloodglucose, with the independent variables discussed above of time, active,signal, blood glucose at a calibration point (BG/cp), and a constant(t_(i)).

The switching between Equations 16, 17, and 18 was determined by theparameters w₁, w₂, and w₃ in equation 5, which was further determined bythe parameters d₁, d₂, and d₃ as given by equations 9-14, where theindividual experts had a linear form:

BG=w ₁ BG ₁ +w ₂ BG ₂ +w ₃ BG ₃  (15)

wherein (BG) was blood glucose, there are three experts (n=3); BG_(i)was the analyte predicted by Expert i; and w_(i) was a parameter, andthe individual Experts BG_(i) were further defined by the expressionshown as Equations 16, 17, and 18

BG ₁ =p ₁(time_(c))+q ₁(active)+r ₁(signal)+s ₁(BG|cp)+t ₁  (16)

BG ₂ =p ₂(time_(c))+q ₂(active)+r ₂(signal)+s ₂(BG|cp)+t ₂  (17)

BG ₃ =p ₃(time_(c))+q ₃(active)+r ₃(signal)+s ₃(BG|cp)+t ₃  (18)

wherein, BG_(i) was the analyte predicted by Expert i; parametersinclude, times (elapsed time since calibration), active (active signal),signal (calibrated signal), and BG/cp (blood glucose value at acalibration point); p_(i), q_(i), r_(i), and s_(i) were coefficients;and t_(i) was a constant; and further where the weighting value, w_(i),was defined by the formulas shown as Equations 19, 20, and 21

$\begin{matrix}{w_{1} = \frac{^{d_{1}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (19) \\{w_{2} = \frac{^{d_{2}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (20) \\{w_{3} = \frac{^{d_{3}}}{^{d_{1}} + ^{d_{2}} + ^{d_{3}}}} & (21)\end{matrix}$

where e referred to the exponential function and d_(i) was a parameterset (analogous to Equations 16, 17, and 18) that were used to determinethe weights w_(i), given by Equations 19, 20, and 21, and

d ₁=τ₁(time_(c))+β₁(active)+γ₁(signal)+δ₁(BG|cp)+∈₁  (22)

d ₂=τ₂(time_(c))+β₂(active)+γ₂(signal)+δ₂(BG|cp)+∈₂  (23)

d ₃=τ₃(time_(c))+β₃(active)+γ₃(signal)+δ₃(BG|cp)+∈₃  (24)

where τ_(i), β_(i), γ_(i), and δ_(i) were coefficients, and where ∈_(i)is a constant.

To calculate the above parameters an optimization method was applied tothe algorithm (Equations 15-24) and the large data set. The optimizationmethod used was the Expectation Maximization method (Dempster, A. P., N.M. Laird, and D. B. Rubin, J. Royal Statistical Society (SeriesB-Methodological) 39:(1), 1977), but other methods may be used as well.

The parameters in these equations were determined such that theposterior probability of the actual glucose was maximized.

Example 4 Prediction of Measurement Values II

A. Calibration Ratio Check

In order to insure an efficacious calibration of the sampling system,the value of the following ratio was found to fall in a selected range:

${CalRatio} = \frac{{BG}/{cp}}{\left( {{{active}/{cp}} + {offset}} \right)}$

where the offset takes into account the intercept value. The range isestablished using standard error minimization routines to evaluate alarge population of calibration points, and thereby determine theCalRatio values which result in accurate blood glucose predictions. Inone embodiment, the preferred CalRatio range of values was between0.00039 and 0.01. In the CalRatio, BG/cp was the blood glucoseconcentration at the calibration point (or calibration time), active wasthe input prediction at the calibration point, and offset was a constantoffset. The offset value was established empirically using standarderror minimization routines to evaluate a number of potential offsetvalues for a large data set, and thereby select the one that, results inthe most accurate prediction of blood glucose.

The CalRatio check provides a screen for valid or efficaciouscalibration readings. If the CalRatio falls outside of the range ofselected values, then the calibration was rejected and the calibrationwas re-done. Low values of this ratio indicated low sensitivity ofglucose detection.

B. Prediction of Values

GlucoWatch® monitors (Cygnus, Inc., Redwood City, Calif., USA) wereapplied to the lower forearm of human subjects with diabetes (requiringinsulin injection). Iontophoretic extraction of glucose was carried outusing the GlucoWatch® monitor which employs (i) a low-leveliontophoretic current to extract glucose through patient's skin, and(ii) an electrochemical biosensor to detect the extracted glucose.

The subjects were 18 years of age, or older, and consisted of both malesand females from a broad ethnic cross-section. Iontophoresis was carriedout for 3 minute intervals and electrochemical detection was carried outfor 7 minute intervals to result in 10 minute measurement cycles—thusgenerating collections of data (data sets) as described in Example 3. Asdescribed in Example 3, the active measurement was the averaged signalfrom two active reservoirs, for example, a first electrode acts as thecathode during the first 10 minute cycle (3 minutes of iontophoresis,followed by 7 minutes of sensing) and a second electrode acts as thecathode during the second 10 minute cycle. The combined cycle requires20 minutes, and the combined cathode sensor data is used as a measure ofthe glucose extracted (an averaged “active signal”, see Example 3). This20 minute cycle is repeated throughout operation of the GlucoWatch®monitor.

In addition, subjects obtained two capillary blood samples per hour, andthe glucose concentration was determined using a HemoCue® clinicalanalyzer (HemoCue AB, Sweden). The blood glucose measurement obtained atthree hours was used as a single point calibration, which was used tocalculate the extracted blood glucose for all subsequent GlucoWatch®monitor measurements.

The data that were used for this analysis were obtained by diabeticsubjects each wearing two GlucoWatch® monitors over a 14 hour period.The MOE inputs consisted of the following parameters (described inExample 3): time_(c), active, signal, blood glucose at a calibrationpoint (BG/cp). For the calibrated signal:

${signal} = {{{BG}/{cp}}\frac{\left( {{active} + {offset}} \right)}{\left( {{{active}/{cp}} + {offset}} \right)}}$

where (i) active/cp was the input prediction at the calibration point,and (ii) the offset and takes into account the fact that when predictedblood glucose is plotted vs. active, there is a non-zero y-intercept.The optimized value of the offset that was used was a constant value of1000 nC. The signal that is used in the Mixtures of Experts algorithm istemperature compensated by applying an Arrhenius type correction to theraw signal data to account for skin temperature fluctuations.

Finally, in order to eliminate potential outlier points, various screenswere applied to the raw and integrated sensor signals. The purpose ofthese screens were to determine whether certain environmental,physiological or technical conditions existed during a measurement cyclethat could result in an erroneous reading. The screens that were usedmeasured the averaged signal (active), iontophoretic voltage,temperature, and skin surface conductance. If any of these measurementsdeviated sufficiently from predefined behavior during a measurement,then the entire measurement was excluded. For example, if the skinsurface conductance exceeded a set threshold, which indicated excessivesweating (sweat contains glucose), then this potentially erroneousmeasurement was excluded. These screens enable very noisy data to beremoved, while enabling the vast majority of points (>87%) to beaccepted.

The Mixtures of Experts was further customized in the following way.When the weights were updated using equations 19-24 (Example 3), aLaplacian distribution function was used. The Laplacian distribution haslonger tails than a Gaussian distribution, and weighs deviationsrelative to the absolute difference from the mean, whereas a Gaussiandistribution weighs deviations relative to the square of difference fromthe mean (P. McCullagh and J. A. Nelder, Generalized Linear Models,Chapman and Hall, 1989; and W. H. Press, S. A. Teukolsky, W. T.Vetterling and B. P. Flannery, Numerical Recipes in C. CambridgeUniversity Press, Cambridge, 1992). In addition, the individual bloodglucose values were weighted by the inverse of the value of the bloodglucose at the calibration point. Both of these modifications result inincreased accuracy of predictions, especially at low blood glucoselevels.

The training data were used to determine the unknown parameters in theMixtures of Experts using the Expectation Maximization Method. TheMixtures of Experts algorithm was trained until convergence of theweights was achieved. The output of the MOE algorithm was the measuredvalue of blood glucose. Using a three hour time point for calibratingthe GlucoWatch® monitor, the mean percentage error (MPE) between theactual blood glucose and the calculated (MOE predicted) blood glucosewas 14.4%.

In a diabetic study consisting of 91 GlucoWatch® monitors, the diabeticsubjects' blood glucose ranged from 40-360 mg/dl. A protocol wasfollowed whereby a subject (who had fasted since the previous midnight)came to a test site where two GlucoWatch® monitors were applied to thesubject, started, and calibrated. Over the next 14 hours, the subjecthad normal meals and a finger prick blood sample was taken every 20minutes for glucose determination (“actual glucose”). Blood glucoselevels were measured using the HemoCue® meter (HemoCue AB, Sweden),which has an accuracy of +10%.

A plot of the glucose levels predicted by the Mixtures of Expertsalgorithm (based on the data described above) versus the actual bloodglucose levels is presented in FIG. 7 (a Correlation Plot). Also shownin FIG. 7 is the orthogonal least squares line (A. Madansky, The Fittingof Straight Lines When both Variables are Subject to Error, J. AmericanStatistical Association 54:173-206, 1959; D. York, Least-Squares Fittingof a Straight Line, Canadian Journal of Physics 44:1079-1986, 1966; W.A. Fuller, Measurement Error Models, Wiley, New York, 1987; and W. H.Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, NumericalRecipes in C. Cambridge University Press, Cambridge, 1992) with an errorvariance ratio (defined as the error in the dependent variable dividedby the error of the independent variable) of 2.05. This variance errorratio corrects the linear regression line (which assumes zero error inthe independent variable) for the true error in both independent anddependent variables.

The variance ratio was determined as follows. Each subject was requiredto wear two GlucoWatch® monitors. Then, at each time point, thedifference between the two watches was determined, squared and dividedby 2. The resulting values were averaged over the total number of timepoints used. Fifty pairs of watches, each with 42 time points, were usedfor this calculation. The error variance for the HemoCue® was obtainedfrom clinical data published in the literature. The GlucoWatch® monitorerror variance was calculated to be 150 (standard deviation=12 mg/dl)and the HemoCue® error variance was calculated to be 73 (standarddeviation=8.5 mg/dl), giving the error ratio of 2.05.

Analysis of the data shown in FIG. 7 showed a slope of 1.04, anintercept of approximately −10.7 mg/dl, and a correlation coefficient ofR=0.89.

It is also instructive to examine graphs of the measured and predictedblood glucose levels vs. time. One such graph is shown in FIG. 8 (in thelegend of FIG. 8: solid diamonds are measurements obtained using theGlucoWatch® monitor; open circles are blood glucose concentrations asdetermined using HemoCue®; and the “star” symbol represents bloodglucose concentration at the calibration point). FIG. 8 indicates theexcellent capabilities of the GlucoWatch® monitor and the Mixtures ofExperts algorithm in calibrating the device.

These statistical results, along with the MPE=14.4% (discussed above),show the excellent predictive capabilities of the GlucoWatch® monitorand the Mixtures of Experts algorithm.

Although preferred embodiments of the subject invention have beendescribed in some detail, it is understood that obvious variations canbe made without departing from the spirit and the scope of the inventionas defined by the appended claims.

1-24. (canceled)
 25. One or more microprocessors for use in an analytemonitoring system for measuring an amount of concentration of analytepresent in a biological system, said one or more microprocessorscomprising programming to control: providing two or more ranges ofmeasurement values, wherein said measurement values are indicative ofamounts or concentration of analyte present in the biological system:identifying the range in which a selected measurement value falls, andemploying an algorithm for prediction of further measurement valueswherein said algorithm is optimized for performance in the identifiedrange.
 26. The one or more microprocessors of claim 25, wherein aMixtures of Experts algorithm is used to determine said selectedmeasurement value and said Mixtures of Experts algorithm is trainedusing a global training set.
 27. The one more microprocessors of claim25, wherein said algorithm for prediction of further measurement valuesis a Mixtures of Experts algorithm and said Mixtures of Expertsalgorithm is trained using data from the identified range.
 28. The oneor more microprocessors of claim 25, wherein said or moremicroprocessors are further programmed to control operation of a sensingdevice that provides raw signal specifically related to analyte amountor concentration in the biological system.
 29. The one or moremicroprocessors of claim 28, wherein said one or more microprocessorsare further programmed to control correlating the raw signal with ameasurement value indicative of analyte amount of concentration in thebiological system.
 30. The one or more microprocessors of claim 29,wherein for the Mixtures of Experts algorithm the individual expertshave a linear form $\begin{matrix}{{An} = {\sum\limits_{i = l}^{n}{{An}_{i}w_{i}}}} & (1)\end{matrix}$ wherein (An) is an analyte of interest, n is the number ofexperts, An_(i) is the analyte predicted by Expert i; and w_(i) is aparameter, and the individual experts An_(i) are further defined by theexpression shown as Equation (2) $\begin{matrix}{{An}_{i} = {{\sum\limits_{j = l}^{m}{a_{ij}P_{j}}} + z_{i}}} & (2)\end{matrix}$ wherein, An_(i) is the analyte predicted by Expert i;P_(j) is one of m parameters, m is typically less then 100; a_(ij) arecoefficients; and z_(i) is a constant; and further where the weightingvalue, w_(i), is defined by the formula shown as Equation (3)$\begin{matrix}{w_{i} = \frac{^{d_{i}}}{\left\lbrack {\sum\limits_{k = l}^{n}^{d_{k}}} \right\rbrack}} & (3)\end{matrix}$ where e refers to the exponential function, d_(i) is oneof the d_(k), d_(i) and d_(k) are parameter sets analogous to Equation 2used to determine the weight w_(i), the d_(k) are given by Equation 4$\begin{matrix}{d_{k} = {{\sum\limits_{j = l}^{m}{\alpha_{jk}P_{j}}} + \omega_{k}}} & (4)\end{matrix}$ where a_(jk) is coefficient, P_(j) is one of m parameters,and where ω_(k) is a constant.
 31. The one or more microprocessors ofclaim 30, wherein the analyte is glucose.
 32. A method to measure anamount of concentration of analyte present in a biological system, themethod comprising: providing two or more ranges of measurement values,in which said measurement values are indicative of amounts orconcentration of analyte present in the biological system; identifyingthe range in which a selected measurement value falls; and employing analgorithm to predict further measurement values in the identified range.33. The method of claim 32, in which the algorithm comprises: for theMixtures of Experts algorithm the individual experts have a linear form$\begin{matrix}{{An} = {\sum\limits_{i = l}^{n}{{An}_{i}w_{i}}}} & (1)\end{matrix}$ wherein (An) is an analyte of interest, n is the number ofexperts, An_(i) is the analyte predicted by Expert i; and w_(i) is aparameter, and the individual experts An_(i) are further defined by theexpression shown as Equation (2) $\begin{matrix}{{An}_{i} = {{\sum\limits_{j = l}^{m}{a_{ij}P_{j}}} + z_{i}}} & (2)\end{matrix}$ wherein, An_(i) is the analyte predicted by Expert i;P_(j) is one of m parameters, m is typically less then 100; a_(ij) arecoefficients; and z_(i) is a constant; and further where the weightingvalue, w_(i), is defined by the formula shown as Equation (3)$\begin{matrix}{w_{i} = \frac{^{d_{i}}}{\left\lbrack {\sum\limits_{k = l}^{n}^{d_{k}}} \right\rbrack}} & (3)\end{matrix}$ where e refers to the exponential function, d_(i) is oneof the d_(k), d_(i) and d_(k) are parameters sets analogous to Equation2 used to determine the weight w_(i), the d_(k) are given by Equation 4$\begin{matrix}{d_{k} = {{\sum\limits_{j = l}^{m}{\alpha_{jk}P_{j}}} + {\omega_{k}.}}} & (4)\end{matrix}$ where a_(jk) is coefficient, P_(j) is one of m parameters,and where ω_(k) is a constant.